Question

What is the missing value in x 1/5 = 6? (1 point)

Answer 1

Solve the following equation: 2^(x+2) = 4^2
. What is the missing value?(1 point)

Answer 2

Solve the following equation: 3^(x−2) = 81
. What is the missing value? (1 point)

Answer 3

To solve the equation \( x \cdot \frac{1}{5} = 6 \), you need to isolate \( x \).

You can do this by multiplying both sides of the equation by 5:

\[
x \cdot \frac{1}{5} \cdot 5 = 6 \cdot 5
\]

This simplifies to:

\[
x = 30
\]

Therefore, the missing value is \( x = 30 \).

Answer 4

To solve the equation \( 2^{(x+2)} = 4^2 \), we first rewrite \( 4^2 \) in terms of base 2:

\[
4 = 2^2 \implies 4^2 = (2^2)^2 = 2^{2 \cdot 2} = 2^4
\]

Now, we can set the exponents equal to each other since the bases are the same:

\[
x + 2 = 4
\]

Next, solve for \( x \) by subtracting 2 from both sides:

\[
x = 4 - 2 = 2
\]

Thus, the missing value is \( x = 2 \).

Answer 5

To solve the equation \( 3^{(x-2)} = 81 \), we first express \( 81 \) as a power of \( 3 \):

\[
81 = 3^4
\]

Now the equation becomes:

\[
3^{(x-2)} = 3^4
\]

Since the bases are the same, we can set the exponents equal to each other:

\[
x - 2 = 4
\]

Next, solve for \( x \) by adding 2 to both sides:

\[
x = 4 + 2 = 6
\]

Thus, the missing value is \( x = 6 \).