Solve for $$ x: $$ $$ \begin{array}{l}5^{x}=41 \ x=\end{array} $$

Question

UpStudy AI · Accepted Answer

We start with the equation
$$
5^x = 41.
$$

**Step 1: Take the natural logarithm of both sides.**

$$
\ln(5^x) = \ln(41)
$$

**Step 2: Use the logarithmic identity $$\ln(a^b) = b\ln(a)$$.**

$$
x \ln(5) = \ln(41)
$$

**Step 3: Solve for $$ x $$ by dividing both sides by $$\ln(5)$$.**

$$
x = \frac{\ln(41)}{\ln(5)}
$$
$$ x = \frac{\ln(41)}{\ln(5)} $$

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