What is the answer to log_{x}(16/25)=2 ?

The answer to log_{x}(16/25)=2 is x=e^{(ln(16/25))/2}

Solve for x: log_{x}(16/25)=2

The solution is x=e^{(ln(16/25))/2}

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lo g_{x} (\frac{16}{25}) = 2

x = e^{\frac{l n ( \frac{16}{25} )}{2}}

Decimal Notation

x = 0.8

Solution steps

lo g_{x} (\frac{16}{25}) = 2

Apply log rules

\frac{ln ( \frac{16}{25} )}{ln ( x )} = 2

Multiply both sides by

ln (x)

\frac{ln ( \frac{16}{25} )}{ln ( x )} ln (x) = 2 ln (x)

Simplify

ln (\frac{16}{25}) = 2 ln (x)

Switch sides

2 ln (x) = ln (\frac{16}{25})

Divide both sides by

2

ln (x) = \frac{ln ( \frac{16}{25} )}{2}

Apply log rules

x = e^{\frac{l n ( \frac{16}{25} )}{2}}

Verify Solutions:

x = e^{\frac{l n ( \frac{16}{25} )}{2}}

True

The solution is

x = e^{\frac{l n ( \frac{16}{25} )}{2}}

5 = - lo g_{\frac{1}{3}} (3 x - 5)

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

lo g_{3} (x) = 7

lo g_{\frac{1}{2}} (x) = 4

- 2 = ln (x)

What is the answer to log_{x}(16/25)=2 ?
The answer to log_{x}(16/25)=2 is x=e^{(ln(16/25))/2}
Solve for x: log_{x}(16/25)=2
The solution is x=e^{(ln(16/25))/2}