What is the answer to log_{9}((x-6)/(x+3))=1 ?

The answer to log_{9}((x-6)/(x+3))=1 is x=-33/8

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log_{9}((x-6)/(x+3))=1

lo g_{9} (\frac{x - 6}{x + 3}) = 1

x = - \frac{33}{8}

Decimal

x = - 4.125

Solution steps

lo g_{9} (\frac{x - 6}{x + 3}) = 1

Apply log rules

\frac{x - 6}{x + 3} = 9^{1}

Multiply both sides by

x + 3

\frac{x - 6}{x + 3} (x + 3) = 9^{1} (x + 3)

Simplify

x - 6 = 9 (x + 3)

Solve

x - 6 = 9 (x + 3) : x = - \frac{33}{8}

x = - \frac{33}{8}

Verify Solutions:

x = - \frac{33}{8}

True

The solution is

x = - \frac{33}{8}

lo g_{x - 2} (9) = 2

lo g_{x} (125) = 9

lo g_{x} (125) = 6

lo g_{x} (125) = 5

3.32 = - lo g_{10} (x)

What is the answer to log_{9}((x-6)/(x+3))=1 ?
The answer to log_{9}((x-6)/(x+3))=1 is x=-33/8
Solve for x: log_{9}((x-6)/(x+3))=1
The solution is x=-33/8