Question

3 exponent x+3 = 8 ( solve for it please)

Answer 1

To solve the equation \( 3^{x + 3} = 8 \), follow these steps:

1. Take the natural logarithm of both sides:
\[
\ln(3^{x + 3}) = \ln(8)
\]

2. Apply the power rule of logarithms:
\[
(x + 3) \ln(3) = \ln(8)
\]

3. Solve for \( x + 3 \):
\[
x + 3 = \frac{\ln(8)}{\ln(3)}
\]

4. Subtract 3 from both sides to solve for \( x \):
\[
x = \frac{\ln(8)}{\ln(3)} - 3
\]

Now, we can calculate the numerical value using a calculator:

- \( \ln(8) \approx 2.0794 \)
- \( \ln(3) \approx 1.0986 \)

Plugging in these values:
\[
x \approx \frac{2.0794}{1.0986} - 3
\]
\[
x \approx 1.8947 - 3
\]
\[
x \approx -1.1053
\]

So the solution for \( x \) is approximately \( -1.1053 \).