What is the answer to log_{m}(sqrt(6))= 1/2 ?

The answer to log_{m}(sqrt(6))= 1/2 is m=6

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log_{m}(sqrt(6))= 1/2

lo g_{m} (6) = \frac{1}{2}

m = 6

Solution steps

lo g_{m} (6) = \frac{1}{2}

Apply log rules

\frac{ln ( 6 )}{ln ( m )} = \frac{1}{2}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

ln (6) \cdot 2 = ln (m) \cdot 1

Apply log rules

6 = m

Switch sides

m = 6

Verify Solutions:

m = 6

True

The solution is

m = 6

1 - 8 ln (\frac{2 x - 1}{7}) = 14

80 = 29.499 \cdot ln (x) - 82.679

24 = 10 lo g_{10} (x)

ln (\frac{1}{x ^{2}}) + ln (x) = 4

ln (4 x) - 3 ln (x^{2}) = ln^{2} (x)

What is the answer to log_{m}(sqrt(6))= 1/2 ?
The answer to log_{m}(sqrt(6))= 1/2 is m=6
Solve for m: log_{m}(sqrt(6))= 1/2
The solution is m=6