What is the answer to log_{x-3}(81)=4 ?

The answer to log_{x-3}(81)=4 is x=6

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log_{x-3}(81)=4

lo g_{x - 3} (81) = 4

x = 6

Solution steps

lo g_{x - 3} (81) = 4

Apply log rules

\frac{1}{lo g _{81} ( x - 3 )} = 4

Multiply both sides by

lo g_{81} (x - 3)

\frac{1}{lo g _{81} ( x - 3 )} lo g_{81} (x - 3) = 4 lo g_{81} (x - 3)

Simplify

1 = 4 lo g_{81} (x - 3)

Switch sides

4 lo g_{81} (x - 3) = 1

Divide both sides by

4

lo g_{81} (x - 3) = \frac{1}{4}

Apply log rules

x - 3 = 3

Solve

x - 3 = 3 : x = 6

x = 6

Verify Solutions:

x = 6

True

The solution is

x = 6

lo g_{5} (5 - x) = lo g_{5} (3)

0 = \frac{1 - ln ( x )}{x ^{2}}

lo g_{x} (8 e^{3}) = 3

lo g_{3} (x^{2}) = 2 lo g_{3} (4) - 4 lo g_{3} (5)

y, ln (2 x + y) = x + 1