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

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

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

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

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

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

Solution steps

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

Apply log rules

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

Multiply both sides by

ln (x)

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

Simplify

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

Switch sides

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

Divide both sides by

2

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

Apply log rules

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

Verify Solutions:

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

True

The solution is

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

3 lo g_{10} (4 - x) = 1 - x

\frac{9}{8} lo g_{2} (x) = - 10

lo g_{a} (3) = 0.565

lo g_{10} (\frac{x}{3} + 50) = 2

lo g_{10} (\frac{x}{5}) + 3 = 5.3

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