What is the answer to log_{x}(16)= 4/5 ?

The answer to log_{x}(16)= 4/5 is x=32

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log_{x}(16)= 4/5

lo g_{x} (16) = \frac{4}{5}

x = 32

Solution steps

lo g_{x} (16) = \frac{4}{5}

Apply log rules

\frac{1}{lo g _{16} ( x )} = \frac{4}{5}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

1 \cdot 5 = lo g_{16} (x) \cdot 4

Simplify

5 = lo g_{16} (x) \cdot 4

Switch sides

lo g_{16} (x) \cdot 4 = 5

Divide both sides by

4

lo g_{16} (x) = \frac{5}{4}

Apply log rules

x = 32

Verify Solutions:

x = 32

True

The solution is

x = 32

d = lo g_{2} (\frac{8}{d})

2 ln (x) - (ln (x))^{2} = 0

lo g_{4} (x + 2) + lo g_{2} (4) = 0

lo g_{3} (x - 4) + lo g_{3} (x + 6) = 1

lo g_{x} (1.41) = 0.5