What is the answer to log_{x}(27)= 3/4 ?

The answer to log_{x}(27)= 3/4 is x=81

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log_{x}(27)= 3/4

lo g_{x} (27) = \frac{3}{4}

x = 81

Solution steps

lo g_{x} (27) = \frac{3}{4}

Apply log rules

\frac{1}{lo g _{27} ( 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_{27} (x) \cdot 3

Simplify

4 = lo g_{27} (x) \cdot 3

Switch sides

lo g_{27} (x) \cdot 3 = 4

Divide both sides by

3

lo g_{27} (x) = \frac{4}{3}

Apply log rules

x = 81

Verify Solutions:

x = 81

True

The solution is

x = 81

lo g_{3} (2 x - 6) = 2

lo g_{10} (- x - 4) + lo g_{10} (3) = 1

lo g_{2} (x + 7) + lo g_{2} (x + 5) = 3

ln (x) + ln (x + 2) = ln (8)

2 lo g_{4} (2 - x) - lo g_{4} (x + 5) = 1