What is the answer to log_{x}(25)= 2/3 ?

The answer to log_{x}(25)= 2/3 is x=125

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log_{x}(25)= 2/3

lo g_{x} (25) = \frac{2}{3}

x = 125

Solution steps

lo g_{x} (25) = \frac{2}{3}

Apply log rules

\frac{1}{lo g _{25} ( 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_{25} (x) \cdot 2

Simplify

3 = lo g_{25} (x) \cdot 2

Switch sides

lo g_{25} (x) \cdot 2 = 3

Divide both sides by

2

lo g_{25} (x) = \frac{3}{2}

Apply log rules

x = 125

Verify Solutions:

x = 125

True

The solution is

x = 125

lo g_{4} (15 x + 1) = 2

lo g_{x} (64) = lo g_{5} (125)

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

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

lo g_{3} (x) - lo g_{9} (4 x) = 1

What is the answer to log_{x}(25)= 2/3 ?
The answer to log_{x}(25)= 2/3 is x=125
Solve for x: log_{x}(25)= 2/3
The solution is x=125