What is the answer to log_{x-1}(4)=2 ?

The answer to log_{x-1}(4)=2 is x=3

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log_{x-1}(4)=2

lo g_{x - 1} (4) = 2

x = 3

Solution steps

lo g_{x - 1} (4) = 2

Apply log rules

\frac{1}{lo g _{4} ( x - 1 )} = 2

Multiply both sides by

lo g_{4} (x - 1)

\frac{1}{lo g _{4} ( x - 1 )} lo g_{4} (x - 1) = 2 lo g_{4} (x - 1)

Simplify

1 = 2 lo g_{4} (x - 1)

Switch sides

2 lo g_{4} (x - 1) = 1

Divide both sides by

2

lo g_{4} (x - 1) = \frac{1}{2}

Apply log rules

x - 1 = 2

Solve

x - 1 = 2 : x = 3

x = 3

Verify Solutions:

x = 3

True

The solution is

x = 3

23 = 10 lo g_{10} (x)

x, f = 1 + lo g_{2} (x + k)

lo g_{2} (N) = - 2

0 = ln (x) + 1

0 = ln (x) + 2