𝑥
.
3−53x=18
3
−
5
3
𝑥
=
18
(1 point)
3 answers
To solve the equation
\[ 3 - 5 \cdot 3^x = 18, \]
first, isolate the term involving \( x \):
\[ -5 \cdot 3^x = 18 - 3. \]
This simplifies to:
\[ -5 \cdot 3^x = 15. \]
Now, divide both sides by -5:
\[ 3^x = -\frac{15}{5} = -3. \]
Since \( 3^x \) (an exponential function) is always positive for real numbers, there is no real solution to the equation \( 3^x = -3 \).
Thus, the final answer is:
No real solution.
Let's solve the equation step by step. The given equation is:
\[ 3 - 5 \cdot 3^x = 18. \]
Isolate the term containing \(3^x\): Subtract 3 from both sides:
\[ -5 \cdot 3^x = 18 - 3 \implies -5 \cdot 3^x = 15. \]
Divide both sides by -5:
\[ 3^x = -\frac{15}{5} \implies 3^x = -3. \]
At this point, we see that \(3^x\) (which represents an exponential function) always yields positive values for real \(x\). Therefore, \(3^x = -3\) has no real solution.
Final conclusion: There is no value of \(x\) that satisfies the equation \(3 - 5 \cdot 3^x = 18\) among real numbers.
If you need help with any other aspect or further clarification, let me know!
