What is the answer to log_{x}(64)= 3/4 ?

The answer to log_{x}(64)= 3/4 is x=256

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log_{x}(64)= 3/4

lo g_{x} (64) = \frac{3}{4}

x = 256

Solution steps

lo g_{x} (64) = \frac{3}{4}

Apply log rules

\frac{1}{lo g _{64} ( x )} = \frac{3}{4}

Apply fraction cross multiply: if

\frac{a}{b} = \frac{c}{d}

then

a \cdot d = b \cdot c

1 \cdot 4 = lo g_{64} (x) \cdot 3

Simplify

4 = lo g_{64} (x) \cdot 3

Switch sides

lo g_{64} (x) \cdot 3 = 4

Divide both sides by

3

lo g_{64} (x) = \frac{4}{3}

Apply log rules

x = 256

Verify Solutions:

x = 256

True

The solution is

x = 256

ln (x^{2}) = 9

lo g_{10} (x) - lo g_{10} (2) = 1

lo g_{6} (8) + 3 = lo g_{6} (x)

x, ln (x^{2} + 4 y^{2}) = 1

lo g_{7} (x) = 3.64

What is the answer to log_{x}(64)= 3/4 ?
The answer to log_{x}(64)= 3/4 is x=256
Solve for x: log_{x}(64)= 3/4
The solution is x=256