What is the answer to log_{x}(1/32)=-5/2 ?

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

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log_{x}(1/32)=-5/2

lo g_{x} (\frac{1}{32}) = - \frac{5}{2}

x = 4

Solution steps

lo g_{x} (\frac{1}{32}) = - \frac{5}{2}

Apply log rules

\frac{ln ( \frac{1}{32} )}{ln ( x )} = - \frac{5}{2}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

ln (\frac{1}{32}) \cdot 2 = - ln (x) \cdot 5

Apply log rules

x = 4

Verify Solutions:

x = 4

True

The solution is

x = 4

x, lo g_{3 x - 4} (k) = 2

- lo g_{10} (x) = 12.603

1.4 = - lo g_{10} (x)

lo g_{10} (9 x - 1) = 2

lo g_{x} (\frac{1}{32}) = - \frac{5}{4}

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