What is the answer to log_{a}(4/9)=2 ?

The answer to log_{a}(4/9)=2 is a=e^{(ln(4/9))/2}

Solve for a: log_{a}(4/9)=2

The solution is a=e^{(ln(4/9))/2}

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lo g_{a} (\frac{4}{9}) = 2

a = e^{\frac{l n ( \frac{4}{9} )}{2}}

Decimal Notation

a = 0.66666 \dots

Solution steps

lo g_{a} (\frac{4}{9}) = 2

Apply log rules

\frac{ln ( \frac{4}{9} )}{ln ( a )} = 2

Multiply both sides by

ln (a)

\frac{ln ( \frac{4}{9} )}{ln ( a )} ln (a) = 2 ln (a)

Simplify

ln (\frac{4}{9}) = 2 ln (a)

Switch sides

2 ln (a) = ln (\frac{4}{9})

Divide both sides by

2

ln (a) = \frac{ln ( \frac{4}{9} )}{2}

Apply log rules

a = e^{\frac{l n ( \frac{4}{9} )}{2}}

Verify Solutions:

a = e^{\frac{l n ( \frac{4}{9} )}{2}}

True

The solution is

a = e^{\frac{l n ( \frac{4}{9} )}{2}}

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

\frac{2 lo g _{2} ( x ) - 3}{3} = 1

lo g_{4} (x^{3} - 3 x) = 1

lo g_{4} (2 x) + lo g_{4} (x - 2) = 2

lo g_{10} (5 x) = - 2

What is the answer to log_{a}(4/9)=2 ?
The answer to log_{a}(4/9)=2 is a=e^{(ln(4/9))/2}
Solve for a: log_{a}(4/9)=2
The solution is a=e^{(ln(4/9))/2}