What is the answer to log_{x}(64)= 2/3 ?

The answer to log_{x}(64)= 2/3 is x=512

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log_{x}(64)= 2/3

lo g_{x} (64) = \frac{2}{3}

x = 512

Solution steps

lo g_{x} (64) = \frac{2}{3}

Apply log rules

\frac{1}{lo g _{64} ( x )} = \frac{2}{3}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

1 \cdot 3 = lo g_{64} (x) \cdot 2

Simplify

3 = lo g_{64} (x) \cdot 2

Switch sides

lo g_{64} (x) \cdot 2 = 3

Divide both sides by

2

lo g_{64} (x) = \frac{3}{2}

Apply log rules

x = 512

Verify Solutions:

x = 512

True

The solution is

x = 512

ln (4 x) - ln (x + 3) = ln (x^{2})

ln (x + 2) + ln (x - 3) = 0

lo g_{10} (3) = lo g_{10} (x + 1)

lo g_{b} (b^{2}) = 2

x, ln (x - y) = 0

What is the answer to log_{x}(64)= 2/3 ?
The answer to log_{x}(64)= 2/3 is x=512
Solve for x: log_{x}(64)= 2/3
The solution is x=512