What is the answer to log_{x}(100)= 2/3 ?

The answer to log_{x}(100)= 2/3 is x=1000

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log_{x}(100)= 2/3

lo g_{x} (100) = \frac{2}{3}

x = 1000

Solution steps

lo g_{x} (100) = \frac{2}{3}

Apply log rules

\frac{1}{lo g _{100} ( x )} = \frac{2}{3}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

1 \cdot 3 = lo g_{100} (x) \cdot 2

Simplify

3 = lo g_{100} (x) \cdot 2

Switch sides

lo g_{100} (x) \cdot 2 = 3

Divide both sides by

2

lo g_{100} (x) = \frac{3}{2}

Apply log rules

x = 1000

Verify Solutions:

x = 1000

True

The solution is

x = 1000

ln (3 x) = 5

ln (3 x) = 7

ln (x^{2} + x) + 1 = ln (x + 1)

ln (x) + ln (x - 1) = ln (4 - x)

ln (- 3 x + 5) = 6

What is the answer to log_{x}(100)= 2/3 ?
The answer to log_{x}(100)= 2/3 is x=1000
Solve for x: log_{x}(100)= 2/3
The solution is x=1000