What is the answer to log_{x}(8)= 3/4 ?

The answer to log_{x}(8)= 3/4 is x=16

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log_{x}(8)= 3/4

lo g_{x} (8) = \frac{3}{4}

x = 16

Solution steps

lo g_{x} (8) = \frac{3}{4}

Apply log rules

\frac{1}{lo g _{8} ( 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_{8} (x) \cdot 3

Simplify

4 = lo g_{8} (x) \cdot 3

Switch sides

lo g_{8} (x) \cdot 3 = 4

Divide both sides by

3

lo g_{8} (x) = \frac{4}{3}

Apply log rules

x = 16

Verify Solutions:

x = 16

True

The solution is

x = 16

lo g_{7} (x) = 3

ln (x) + ln (x - 2) = ln (4)

ln (x - 1) + ln (x + 2) = 1

5 lo g_{10} (x - 2) = 11

lo g_{x} (2) = 1