Solve Exponential Equation: (3^x + 6^x) / 6^x = 3/2

Published on February 28, 2026

Algebra

Solve the exponential equation by simplifying the fraction using exponent rules to isolate the term (1/2)^x and find the value of x.

Question

Answer

The problem is to solve the following exponential equation for

Here is the step-by-step solution:

Step 1: Separate the fraction on the left side.
We can split the fraction by dividing each term in the numerator by the denominator:

Step 2: Simplify the terms.
We use the property

and note that

(assuming

, which is always true).

Step 3: Simplify the base of the exponential term.

Step 4: Isolate the exponential term.
Subtract 1 from both sides of the equation:

Step 5: Solve for .
Since the bases are the same and equal to

, the exponents must be equal:

Verification (Optional):
Substitute

back into the original equation:

Simplifying the fraction

by dividing the numerator and denominator by 3:

This matches the right side of the original equation.

The solution is

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