What is the answer to log_{X}(2/3)=4 ?

The answer to log_{X}(2/3)=4 is X=e^{(ln(2/3))/4}

Solve for X: log_{X}(2/3)=4

The solution is X=e^{(ln(2/3))/4}

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lo g_{X} (\frac{2}{3}) = 4

X = e^{\frac{l n ( \frac{2}{3} )}{4}}

Decimal Notation

X = 0.90360 \dots

Solution steps

lo g_{X} (\frac{2}{3}) = 4

Apply log rules

\frac{ln ( \frac{2}{3} )}{ln ( X )} = 4

Multiply both sides by

ln (X)

\frac{ln ( \frac{2}{3} )}{ln ( X )} ln (X) = 4 ln (X)

Simplify

ln (\frac{2}{3}) = 4 ln (X)

Switch sides

4 ln (X) = ln (\frac{2}{3})

Divide both sides by

4

ln (X) = \frac{ln ( \frac{2}{3} )}{4}

Apply log rules

X = e^{\frac{l n ( \frac{2}{3} )}{4}}

Verify Solutions:

X = e^{\frac{l n ( \frac{2}{3} )}{4}}

True

The solution is

X = e^{\frac{l n ( \frac{2}{3} )}{4}}

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

lo g_{3} (6 x + 34) = lo g_{3} (- 2)

lo g_{10} (4 x) + 13 = 14

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

lo g_{n} (\frac{1}{8}) = - 3

What is the answer to log_{X}(2/3)=4 ?
The answer to log_{X}(2/3)=4 is X=e^{(ln(2/3))/4}
Solve for X: log_{X}(2/3)=4
The solution is X=e^{(ln(2/3))/4}