What is the answer to log_{a}(32)=-5/2 ?

The answer to log_{a}(32)=-5/2 is a= 1/4

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log_{a}(32)=-5/2

lo g_{a} (32) = - \frac{5}{2}

a = \frac{1}{4}

Decimal Notation

a = 0.25

Solution steps

lo g_{a} (32) = - \frac{5}{2}

Apply log rules

\frac{1}{lo g _{32} ( a )} = - \frac{5}{2}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

1 \cdot 2 = - lo g_{32} (a) \cdot 5

Simplify

2 = - lo g_{32} (a) \cdot 5

Switch sides

- lo g_{32} (a) \cdot 5 = 2

Divide both sides by

- 5

lo g_{32} (a) = - \frac{2}{5}

Apply log rules

a = \frac{1}{4}

Verify Solutions:

a = \frac{1}{4}

True

The solution is

a = \frac{1}{4}

3.5 = - lo g_{10} (c)

N, x = lo g_{a} (N)

lo g_{3} (1 + lo g_{3} (2 x - 7)) = 1

ln (x - 8) = 5

lo g_{5} (x^{2} + 10 x + 1) = 2

What is the answer to log_{a}(32)=-5/2 ?
The answer to log_{a}(32)=-5/2 is a= 1/4
Solve for a: log_{a}(32)=-5/2
The solution is a= 1/4