What is the answer to log_{4}(7/x)=3 ?

The answer to log_{4}(7/x)=3 is x= 7/64

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log_{4}(7/x)=3

lo g_{4} (\frac{7}{x}) = 3

x = \frac{7}{64}

Decimal

x = 0.109375

Solution steps

lo g_{4} (\frac{7}{x}) = 3

Apply log rules

\frac{7}{x} = 4^{3}

Multiply both sides by

x

\frac{7}{x} x = 4^{3} x

Simplify

7 = 64 x

Solve

7 = 64 x : x = \frac{7}{64}

x = \frac{7}{64}

Verify Solutions:

x = \frac{7}{64}

True

The solution is

x = \frac{7}{64}

lo g_{5} (3 x + 10) = 2

ln (x) + ln (x - 1) = 3

lo g_{x} (6) = 5

lo g_{8} (x^{2} - 7 x) = 1

lo g_{x} (\frac{1}{1000}) = 3