What is the answer to log_{1+x}(16)=2 ?

The answer to log_{1+x}(16)=2 is x=3

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log_{1+x}(16)=2

lo g_{1 + x} (16) = 2

x = 3

Solution steps

lo g_{1 + x} (16) = 2

Apply log rules

\frac{1}{lo g _{16} ( 1 + x )} = 2

Multiply both sides by

lo g_{16} (1 + x)

\frac{1}{lo g _{16} ( 1 + x )} lo g_{16} (1 + x) = 2 lo g_{16} (1 + x)

Simplify

1 = 2 lo g_{16} (1 + x)

Switch sides

2 lo g_{16} (1 + x) = 1

Divide both sides by

2

lo g_{16} (1 + x) = \frac{1}{2}

Apply log rules

1 + x = 4

Solve

1 + x = 4 : x = 3

x = 3

Verify Solutions:

x = 3

True

The solution is

x = 3

lo g_{x + 1} (8) = 2

(ln (x))^{2} = 2 ln (x) + 3

lo g_{6} (y) = 3

lo g_{10} (2 x) = 4

ln (10 x) + 1 = 0