What is the answer to log_{b}(4)= 2/3 ?

The answer to log_{b}(4)= 2/3 is b=8

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log_{b}(4)= 2/3

lo g_{b} (4) = \frac{2}{3}

b = 8

Solution steps

lo g_{b} (4) = \frac{2}{3}

Apply log rules

\frac{1}{lo g _{4} ( b )} = \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_{4} (b) \cdot 2

Simplify

3 = lo g_{4} (b) \cdot 2

Switch sides

lo g_{4} (b) \cdot 2 = 3

Divide both sides by

2

lo g_{4} (b) = \frac{3}{2}

Apply log rules

b = 8

Verify Solutions:

b = 8

True

The solution is

b = 8

ln (x) + ln (x - 2) = ln (35)

ln (a) = 2

lo g_{5} (lo g_{3} (x)) = 0

lo g_{5} (x) + lo g_{x} (25) = 3

lo g_{4} (x - 7) = 1 - lo g_{4} (x - 4)