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Popular >

log_{x}(3)=e^2

Solution

lo g_{x} (3) = e^{2}

Solution

x = 3^{\frac{1}{e ^{2}}}

+1

Decimal Notation

x = 1.16030 \dots

Solution steps

lo g_{x} (3) = e^{2}

Apply log rules

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

Multiply both sides by

lo g_{3} (x)

\frac{1}{lo g _{3} ( x )} lo g_{3} (x) = e^{2} lo g_{3} (x)

Simplify

1 = e^{2} lo g_{3} (x)

Switch sides

e^{2} lo g_{3} (x) = 1

Divide both sides by

e^{2}

lo g_{3} (x) = \frac{1}{e ^{2}}

Apply log rules

x = 3^{\frac{1}{e ^{2}}}

Verify Solutions:

x = 3^{\frac{1}{e ^{2}}}

True

The solution is

x = 3^{\frac{1}{e ^{2}}}

Popular Examples

5=1+3.32log_{10}(x)

5 = 1 + 3.32 lo g_{10} (x)

ln(x)=-2.81*600+1.7

ln (x) = - 2.81 \cdot 600 + 1.7

lo g_{2} (1 + x) = b

4log_{2}(3)=log_{2}(x)

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

log_{4}((x^5)/3)=2

lo g_{4} (\frac{x ^{5}}{3}) = 2

Frequently Asked Questions (FAQ)

What is the answer to log_{x}(3)=e^2 ?
The answer to log_{x}(3)=e^2 is x=3^{1/(e^2)}