What is the answer to log_{x}(16)=8 ?

The answer to log_{x}(16)=8 is x=sqrt(2)

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log_{x}(16)=8

lo g_{x} (16) = 8

x = 2

Decimal

x = 1.41421 \dots

Solution steps

lo g_{x} (16) = 8

Apply log rules

\frac{1}{lo g _{16} ( x )} = 8

Multiply both sides by

lo g_{16} (x)

\frac{1}{lo g _{16} ( x )} lo g_{16} (x) = 8 lo g_{16} (x)

Simplify

1 = 8 lo g_{16} (x)

Switch sides

8 lo g_{16} (x) = 1

Divide both sides by

8

lo g_{16} (x) = \frac{1}{8}

Apply log rules

x = 2

Verify Solutions:

x = 2

True

The solution is

x = 2

lo g_{x} (15625) = 3

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

lo g_{7} (2 x + 3) = 1

\frac{1}{3 - lo g _{10} ( x )} + \frac{1}{1 + lo g _{10} ( x )} = 1

lo g_{10} (w - 12) = 4.9