What is the answer to log_{b}(sqrt(27))=-0.5 ?

The answer to log_{b}(sqrt(27))=-0.5 is b= 1/27

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log_{b}(sqrt(27))=-0.5

lo g_{b} (27) = - 0.5

b = \frac{1}{27}

Decimal

b = 0.03703 \dots

Solution steps

lo g_{b} (27) = - 0.5

Apply log rules

\frac{ln ( 27 )}{ln ( b )} = - 0.5

Multiply both sides by

ln (b)

\frac{ln ( 27 )}{ln ( b )} ln (b) = - 0.5 ln (b)

Apply log rules

b = \frac{1}{27}

Verify Solutions:

b = \frac{1}{27}

True

The solution is

b = \frac{1}{27}

lo g_{10} (x) - lo g_{10} (3) = 1

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

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

6 lo g_{x} (27) = 18

lo g_{10} (x) + lo g_{10} (x + 4) = 5

What is the answer to log_{b}(sqrt(27))=-0.5 ?
The answer to log_{b}(sqrt(27))=-0.5 is b= 1/27
Solve for b: log_{b}(sqrt(27))=-0.5
The solution is b= 1/27