What is the answer to log_{x}(32)= 5/3 ?

The answer to log_{x}(32)= 5/3 is x=8

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log_{x}(32)= 5/3

lo g_{x} (32) = \frac{5}{3}

x = 8

Solution steps

lo g_{x} (32) = \frac{5}{3}

Apply log rules

\frac{1}{lo g _{32} ( x )} = \frac{5}{3}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

1 \cdot 3 = lo g_{32} (x) \cdot 5

Simplify

3 = lo g_{32} (x) \cdot 5

Switch sides

lo g_{32} (x) \cdot 5 = 3

Divide both sides by

5

lo g_{32} (x) = \frac{3}{5}

Apply log rules

x = 8

Verify Solutions:

x = 8

True

The solution is

x = 8

lo g_{5} (3 x + 1) = - 2

lo g_{10} (x + 1) + lo g_{10} (2) = lo g_{10} (5 x)

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

lo g_{x + 1} (x^{2} - 3 x + 1) = 1

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