What is the answer to log_{x+1}(64)=2 ?

The answer to log_{x+1}(64)=2 is x=7

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log_{x+1}(64)=2

lo g_{x + 1} (64) = 2

x = 7

Solution steps

lo g_{x + 1} (64) = 2

Apply log rules

\frac{1}{lo g _{64} ( x + 1 )} = 2

Multiply both sides by

lo g_{64} (x + 1)

\frac{1}{lo g _{64} ( x + 1 )} lo g_{64} (x + 1) = 2 lo g_{64} (x + 1)

Simplify

1 = 2 lo g_{64} (x + 1)

Switch sides

2 lo g_{64} (x + 1) = 1

Divide both sides by

2

lo g_{64} (x + 1) = \frac{1}{2}

Apply log rules

x + 1 = 8

Solve

x + 1 = 8 : x = 7

x = 7

Verify Solutions:

x = 7

True

The solution is

x = 7

ln (x) = 10.09876582

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

ln (x^{6}) - ln (x^{2}) = 4

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

1 0^{l o g_{10} (a)} = a