What is the answer to log_{x}(64)=4 ?

The answer to log_{x}(64)=4 is x=2sqrt(2)

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log_{x}(64)=4

lo g_{x} (64) = 4

x = 22

Decimal Notation

x = 2.82842 \dots

Solution steps

lo g_{x} (64) = 4

Apply log rules

\frac{1}{lo g _{64} ( x )} = 4

Multiply both sides by

lo g_{64} (x)

\frac{1}{lo g _{64} ( x )} lo g_{64} (x) = 4 lo g_{64} (x)

Simplify

1 = 4 lo g_{64} (x)

Switch sides

4 lo g_{64} (x) = 1

Divide both sides by

4

lo g_{64} (x) = \frac{1}{4}

Apply log rules

x = 22

Verify Solutions:

x = 22

True

The solution is

x = 22

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

lo g_{x} (16) = \frac{2}{3}

lo g_{5} (2 x + 3) = lo g_{5} (3)

10 = - lo g_{10} (x)

lo g_{x} (25) = - 2