Find the solution for $$ x $$ in the equation $$ 2(3)^{x}=8 $$ $$ x=-1.262 $$ $$ x=1.262 $$ $$ x=0.631 $$ $$ x=-0.631 $$

Question

UpStudy AI · Accepted Answer

To solve the equation $$ 2(3)^x = 8 $$ for $$ x $$, follow these steps:

1. **Isolate the exponential term:**
   $$
   2(3)^x = 8 \implies (3)^x = \frac{8}{2} = 4
   $$

2. **Take the natural logarithm (ln) of both sides:**
   $$
   \ln(3^x) = \ln(4)
   $$

3. **Use the logarithm power rule ($$ \ln(a^b) = b \ln(a) $$):**
   $$
   x \ln(3) = \ln(4)
   $$

4. **Solve for $$ x $$:**
   $$
   x = \frac{\ln(4)}{\ln(3)} \approx \frac{1.3863}{1.0986} \approx 1.262
   $$

Therefore, the correct solution is:

**$$ x = 1.262 $$**
$$ x = 1.262 $$

Find the solution for in the equation