Of course! Please provide the text that you would like me to rewrite without abbreviations.
can you rewrite it without abbreviations
9 answers
- Start with the equation:
\[
3.5 \cdot 1.2^x = 5.4
\]
- Divide both sides by :
\[
1.2^x = \frac{5.4}{3.5}
\]
### Step 2: Simplify the Right Side
- Calculate :
\[
1.2^x = 1.542857 \quad (\text{approximately})
\]
### Step 3: Take the Logarithm
- Apply logarithm to both sides (we can use common logarithm or natural logarithm ):
\[
\log(1.2^x) = \log(1.542857)
\]
### Step 4: Use the Power Rule
- Using the power rule :
\[
x \cdot \log(1.2) = \log(1.542857)
\]
### Step 5: Solve for
- Rearrange to solve for :
\[
x = \frac{\log(1.542857)}{\log(1.2)}
\]
### Step 6: Calculate the Values
- Use a calculator to find the logarithmic values and compute :
-
-
Using these values:
\[
x \approx \frac{0.187}{0.079} \approx 2.37 \quad (\text{approximately})
\]
### Final Answer
Thus, the solution is:
\[
x \approx 2.37
\]
Certainly! Here is the rewritten text without abbreviations:
Step 1: Isolate the Exponential Term
- Start with the equation: \[ 3.5 \cdot 1.2^x = 5.4 \]
- Divide both sides by three point five: \[ 1.2^x = \frac{5.4}{3.5} \]
Step 2: Simplify the Right Side
- Calculate the right side: \[ 1.2^x = 1.542857 \quad (\text{approximately}) \]
Step 3: Take the Logarithm
- Apply logarithm to both sides (we can use the common logarithm or the natural logarithm): \[ \log(1.2^x) = \log(1.542857) \]
Step 4: Use the Power Rule
- Using the power rule: \[ x \cdot \log(1.2) = \log(1.542857) \]
Step 5: Solve for \( x \)
- Rearrange to solve for \( x \): \[ x = \frac{\log(1.542857)}{\log(1.2)} \]
Step 6: Calculate the Values
- Use a calculator to find the logarithmic values and compute \( x \):
- \( \log(1.542857) \)
- \( \log(1.2) \)
Using these values: \[ x \approx \frac{0.187}{0.079} \approx 2.37 \quad (\text{approximately}) \]
Final Answer
Thus, the solution is: \[ x \approx 2.37 \]
Sure! Here is the rewritten text without abbreviations, while maintaining clarity and detail:
Step 1: Isolate the Exponential Term
- Start with the equation: \[ 3.5 \cdot 1.2^x = 5.4 \]
- Divide both sides by three point five: \[ 1.2^x = \frac{5.4}{3.5} \]
Step 2: Simplify the Right Side
- Calculate the value of \(\frac{5.4}{3.5}\): \[ 1.2^x = 1.542857 \quad (\text{approximately}) \]
Step 3: Take the Logarithm
- Apply logarithm to both sides (we can use the common logarithm or the natural logarithm): \[ \log(1.2^x) = \log(1.542857) \]
Step 4: Use the Power Rule
- Using the power rule, which states that \(\log(a^b) = b \cdot \log(a)\): \[ x \cdot \log(1.2) = \log(1.542857) \]
Step 5: Solve for \( x \)
- Rearrange the equation to solve for \( x \): \[ x = \frac{\log(1.542857)}{\log(1.2)} \]
Step 6: Calculate the Values
- Use a calculator to find the logarithmic values and compute \( x \):
- \( \log(1.542857) \approx 0.187 \)
- \( \log(1.2) \approx 0.079 \)
Using these values: \[ x \approx \frac{0.187}{0.079} \approx 2.37 \quad (\text{approximately}) \]
Final Answer
Thus, the solution is: \[ x \approx 2.37 \]
Certainly! Here is the text rewritten without any shortened words or abbreviations:
Step 1: Isolate the Exponential Term
- Begin with the equation: \[ 3.5 \cdot 1.2^x = 5.4 \]
- Divide both sides by three point five: \[ 1.2^x = \frac{5.4}{3.5} \]
Step 2: Simplify the Right Side
- Calculate the value of the fraction, five point four divided by three point five: \[ 1.2^x = 1.542857 \quad (\text{approximately}) \]
Step 3: Take the Logarithm
- Apply the logarithm to both sides (one may use the common logarithm or the natural logarithm): \[ \log(1.2^x) = \log(1.542857) \]
Step 4: Use the Power Rule
- Using the power rule, which states that the logarithm of a number raised to a power is equal to the power multiplied by the logarithm of the base: \[ x \cdot \log(1.2) = \log(1.542857) \]
Step 5: Solve for \( x \)
- Rearrange the equation to solve for the variable \( x \): \[ x = \frac{\log(1.542857)}{\log(1.2)} \]
Step 6: Calculate the Values
- Use a calculator to find the logarithmic values and compute \( x \):
- The logarithm of one point five four two eight five seven is approximately zero point one eight seven.
- The logarithm of one point two is approximately zero point zero seven nine.
Using these values: \[ x \approx \frac{0.187}{0.079} \approx 2.37 \quad (\text{approximately}) \]
Final Answer
Thus, the solution is: \[ x \approx 2.37 \]
Certainly! Here is the text rewritten without using the terms for multiplication, division, or approximation:
Step 1: Isolate the Exponential Term
- Begin with the equation: \[ 3.5 times 1.2 raised to the power of x equals 5.4 \]
- Divide both sides by three point five: \[ 1.2 raised to the power of x equals five point four divided by three point five \]
Step 2: Simplify the Right Side
- Calculate the value of the fraction, five point four divided by three point five: \[ 1.2 raised to the power of x equals approximately one point five four two eight five seven \]
Step 3: Take the Logarithm
- Apply the logarithm to both sides (one may use the common logarithm or the natural logarithm): \[ log(1.2 raised to the power of x) equals log(1.542857) \]
Step 4: Use the Power Rule
- Using the power rule, which states that the logarithm of a number raised to a power is equal to the power multiplied by the logarithm of the base: \[ x times log(1.2) equals log(1.542857) \]
Step 5: Solve for x
- Rearrange the equation to solve for the variable x: \[ x equals log(1.542857) divided by log(1.2) \]
Step 6: Calculate the Values
- Use a calculator to find the logarithmic values and compute x:
- The logarithm of one point five four two eight five seven is approximately zero point one eight seven.
- The logarithm of one point two is approximately zero point zero seven nine.
Using these values: \[ x is approximately equal to zero point one eight seven divided by zero point zero seven nine, which is approximately two point three seven \]
Final Answer
Thus, the solution is: \[ x is approximately equal to two point three seven \]