What is the answer to solvefor a,log_{a}(b)=3 ?

The answer to solvefor a,log_{a}(b)=3 is a=e^{(ln(b))/3} {0 1}

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solvefor a,log_{a}(b)=3

solve for

a, lo g_{a} (b) = 3

a = e^{\frac{l n ( b )}{3}} {0 < b < 1 or b > 1}

Solution steps

lo g_{a} (b) = 3

Apply log rules

\frac{ln ( b )}{ln ( a )} = 3

Multiply both sides by

ln (a)

\frac{ln ( b )}{ln ( a )} ln (a) = 3 ln (a)

Simplify

ln (b) = 3 ln (a)

Switch sides

3 ln (a) = ln (b)

Divide both sides by

3

ln (a) = \frac{ln ( b )}{3}

Apply log rules

a = e^{\frac{l n ( b )}{3}}

Verify Solutions:

a = e^{\frac{l n ( b )}{3}} {0 < b < 1 or b > 1}

The solution is

a = e^{\frac{l n ( b )}{3}} {0 < b < 1 or b > 1}

lo g_{x} (64) = 4

lo g_{6} (x) + lo g_{6} (x - 1) = 1

lo g_{x} (16) = \frac{2}{3}

lo g_{5} (2 x + 3) = lo g_{5} (3)

10 = - lo g_{10} (x)

What is the answer to solvefor a,log_{a}(b)=3 ?
The answer to solvefor a,log_{a}(b)=3 is a=e^{(ln(b))/3} {0<b<1\lor b>1}