What is the answer to log_{a}(27/8)=1.5 ?

The answer to log_{a}(27/8)=1.5 is a=e^{(2ln(27/8))/3}

Solve for a: log_{a}(27/8)=1.5

The solution is a=e^{(2ln(27/8))/3}

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lo g_{a} (\frac{27}{8}) = 1.5

a = e^{\frac{2 l n ( \frac{27}{8} )}{3}}

Decimal Notation

a = 2.25

Solution steps

lo g_{a} (\frac{27}{8}) = 1.5

Apply log rules

\frac{ln ( \frac{27}{8} )}{ln ( a )} = 1.5

Multiply both sides by

ln (a)

\frac{ln ( \frac{27}{8} )}{ln ( a )} ln (a) = 1.5 ln (a)

Simplify

ln (\frac{27}{8}) = 1.5 ln (a)

Switch sides

1.5 ln (a) = ln (\frac{27}{8})

Multiply both sides by

10

15 ln (a) = ln (\frac{27}{8}) \cdot 10

Divide both sides by

15

ln (a) = \frac{2 ln ( \frac{27}{8} )}{3}

Apply log rules

a = e^{\frac{2 l n ( \frac{27}{8} )}{3}}

Verify Solutions:

a = e^{\frac{2 l n ( \frac{27}{8} )}{3}}

True

The solution is

a = e^{\frac{2 l n ( \frac{27}{8} )}{3}}

200 = lo g_{10} (\frac{x}{2})

lo g_{- b} (64) = 2

lo g_{10} (x) = - 5.6

lo g_{10} (x) = - 5.7

lo g_{10} (x) = - 5.4

What is the answer to log_{a}(27/8)=1.5 ?
The answer to log_{a}(27/8)=1.5 is a=e^{(2ln(27/8))/3}
Solve for a: log_{a}(27/8)=1.5
The solution is a=e^{(2ln(27/8))/3}