Explain how to solve 3^x-4 = 6 using the change of base formula . Include the solution for x in your answer. Round your answer to the nearest thousandth.




To solve the equation \( 3^x - 4 = 6 \) using the change of base formula, follow these steps:

### Step 1: Isolate the exponential term
First, add 4 to both sides of the equation to isolate the exponential expression:

\[
3^x - 4 + 4 = 6 + 4
\]

\[
3^x = 10
\]

### Step 2: Apply logarithms to solve for \( x \)
To solve for \( x \), take the logarithm of both sides. You can use any logarithm base, but the common logarithm (base 10) or natural logarithm (base \( e \)) are most common. Let's use the natural logarithm:

\[
\ln(3^x) = \ln(10)
\]

### Step 3: Use the power rule of logarithms
Apply the power rule of logarithms, which states \( \ln(a^b) = b \cdot \ln(a) \),

Learn how to solve the equation 3^x - 4 = 6 using the change of base formula. Follow a detailed step-by-step solution including the application of logarithms to isolate and solve for x. Suitable for Grades 10-12.

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