What is the answer to log_{x-5}(25)=2 ?

The answer to log_{x-5}(25)=2 is x=10

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log_{x-5}(25)=2

lo g_{x - 5} (25) = 2

x = 10

Solution steps

lo g_{x - 5} (25) = 2

Apply log rules

\frac{1}{lo g _{25} ( x - 5 )} = 2

Multiply both sides by

lo g_{25} (x - 5)

\frac{1}{lo g _{25} ( x - 5 )} lo g_{25} (x - 5) = 2 lo g_{25} (x - 5)

Simplify

1 = 2 lo g_{25} (x - 5)

Switch sides

2 lo g_{25} (x - 5) = 1

Divide both sides by

2

lo g_{25} (x - 5) = \frac{1}{2}

Apply log rules

x - 5 = 5

Solve

x - 5 = 5 : x = 10

x = 10

Verify Solutions:

x = 10

True

The solution is

x = 10

ln (\frac{x}{x - 1}) = 1

10 = 10 lo g_{10} (x)

ln (y) = 0.66

2 lo g_{5} (x) = - lo g_{5} (25)

x, ln (x) = y + 2