What is the answer to log_{x}(7)= 1/3 ?

The answer to log_{x}(7)= 1/3 is x=343

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log_{x}(7)= 1/3

lo g_{x} (7) = \frac{1}{3}

x = 343

Solution steps

lo g_{x} (7) = \frac{1}{3}

Apply log rules

\frac{1}{lo g _{7} ( x )} = \frac{1}{3}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

1 \cdot 3 = lo g_{7} (x) \cdot 1

Simplify

3 = lo g_{7} (x)

Apply log rules

343 = x

Switch sides

x = 343

Verify Solutions:

x = 343

True

The solution is

x = 343

- 3 = lo g_{x} (\frac{1}{8})

x, y = lo g_{g} (x)

80 = 20 lo g_{10} (G)

lo g_{10} (x) (100) = 2

lo g_{x} (16) = 8