What is the answer to log_{x-3}(25)=2 ?

The answer to log_{x-3}(25)=2 is x=8

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log_{x-3}(25)=2

lo g_{x - 3} (25) = 2

x = 8

Solution steps

lo g_{x - 3} (25) = 2

Apply log rules

\frac{1}{lo g _{25} ( x - 3 )} = 2

Multiply both sides by

lo g_{25} (x - 3)

\frac{1}{lo g _{25} ( x - 3 )} lo g_{25} (x - 3) = 2 lo g_{25} (x - 3)

Simplify

1 = 2 lo g_{25} (x - 3)

Switch sides

2 lo g_{25} (x - 3) = 1

Divide both sides by

2

lo g_{25} (x - 3) = \frac{1}{2}

Apply log rules

x - 3 = 5

Solve

x - 3 = 5 : x = 8

x = 8

Verify Solutions:

x = 8

True

The solution is

x = 8

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

lo g_{10} (2 x - 3) = 2

lo g_{x} (0.5) = - 1

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

lo g_{4} (x - 6) + 1 = 3 - lo g_{4} (x)