# Solve the logarithmic equation algebraically. Approximate the result to three decimal places. (If there is no solution, enter NO SOLUTION.)log 3 x + log(x + 5) = log 3(x + 32)

Question
9 views help_outlineImage TranscriptioncloseSolve the logarithmic equation algebraically. Approximate the result to three decimal places. (If there is no solution, enter NO SOLUTION.) log 3 x + log(x + 5) = log 3(x + 32) fullscreen
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Step 1

A property:

The following are two properties of logarithm of two numbers, m and n at a given base, say c:

Step 2

Calculation:

Here, the base of the logarithm is c = 3; the numbers are m = x, n = x + 32.

Step 3

Note:

The logarithm of a non-positive quantity is not defined. The log function is defined only for positive numbers.

For x = –8, the left hand side (LHS) of the given equation would have the terms:

log3 x = log3 –8;

log3 (x + 5) = log3 (–8 + 5) = log3 &ndash...

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