What is the answer to log_{b}(5)= 1/4 ?

The answer to log_{b}(5)= 1/4 is b=625

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log_{b}(5)= 1/4

lo g_{b} (5) = \frac{1}{4}

b = 625

Solution steps

lo g_{b} (5) = \frac{1}{4}

Apply log rules

\frac{1}{lo g _{5} ( b )} = \frac{1}{4}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

1 \cdot 4 = lo g_{5} (b) \cdot 1

Simplify

4 = lo g_{5} (b)

Apply log rules

625 = b

Switch sides

b = 625

Verify Solutions:

b = 625

True

The solution is

b = 625

6 - 4.79 = 5 lo g_{10} (d - 5)

lo g_{2} (x^{2} + 5 x + 7) = 0

lo g_{5} (p) = 1.5

ln (2 x + 1) + ln (- x + 1) = 0

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