Score: 7/16 Answered: 7/16 Question 8 Solve for $$ x: 5^{x}=38 $$ $$ x= $$ $$ \square $$ Basic Funcs Trig

Question

UpStudy AI · Accepted Answer

Below is a step-by-step solution.

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### Step 1: Write the Equation

We start with the equation:
$$
5^x = 38
$$

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### Step 2: Take the Logarithm of Both Sides

To solve for $$ x $$, take the natural logarithm on both sides of the equation:
$$
\ln(5^x) = \ln(38)
$$

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### Step 3: Use the Power Rule of Logarithms

Recall the power rule of logarithms, which states:
$$
\ln(a^b) = b \ln(a)
$$
Apply this rule:
$$
x \ln(5) = \ln(38)
$$

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### Step 4: Solve for $$ x $$

Isolate $$ x $$ by dividing both sides by $$ \ln(5) $$:
$$
x = \frac{\ln(38)}{\ln(5)}
$$

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### Final Answer

$$
x = \frac{\ln(38)}{\ln(5)}
$$
$$ x = \frac{\ln(38)}{\ln(5)} $$

Score: 7/16 Answered: 7/16 Question 8 Solve for \( x: 5^{x}=38 \) \[ x= \] \( \square \) Basic Funcs Trig