What is the answer to log_{x}(16/625)=4 ?

The answer to log_{x}(16/625)=4 is x=e^{(ln(16/625))/4}

Solve for x: log_{x}(16/625)=4

The solution is x=e^{(ln(16/625))/4}

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lo g_{x} (\frac{16}{625}) = 4

x = e^{\frac{l n ( \frac{16}{625} )}{4}}

Decimal Notation

x = 0.4

Solution steps

lo g_{x} (\frac{16}{625}) = 4

Apply log rules

\frac{ln ( \frac{16}{625} )}{ln ( x )} = 4

Multiply both sides by

ln (x)

\frac{ln ( \frac{16}{625} )}{ln ( x )} ln (x) = 4 ln (x)

Simplify

ln (\frac{16}{625}) = 4 ln (x)

Switch sides

4 ln (x) = ln (\frac{16}{625})

Divide both sides by

4

ln (x) = \frac{ln ( \frac{16}{625} )}{4}

Apply log rules

x = e^{\frac{l n ( \frac{16}{625} )}{4}}

Verify Solutions:

x = e^{\frac{l n ( \frac{16}{625} )}{4}}

True

The solution is

x = e^{\frac{l n ( \frac{16}{625} )}{4}}

ln (4 x) - ln (x^{6}) = ln (2)

e \cdot ln (x - 10) = x - 10

d, 5 ln (d^{2} + y x) = 7

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

ln (x^{2}) + ln (x) = 2

What is the answer to log_{x}(16/625)=4 ?
The answer to log_{x}(16/625)=4 is x=e^{(ln(16/625))/4}
Solve for x: log_{x}(16/625)=4
The solution is x=e^{(ln(16/625))/4}