Solve Logarithm Equation log base 3 of 27 equals x plus 2

Published on February 28, 2026

Algebra

Learn how to solve the logarithmic equation log base 3 of 27 equals x plus 2 by simplifying the logarithm and solving for x.

Question

Answer

The given equation is:

We need to solve for

First, we can simplify the left side of the equation, which is

.
Since

, we have

Now, the equation becomes:

Subtract 2 from both sides of the equation to isolate

Therefore,

Final Answer: The final answer is

Theorems

• Definition of Logarithm

The logarithm of a number

to the base

is the exponent to which

must be raised to produce

. Mathematically, if

, then

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