What is the answer to ln(log_{x}(3))=2 ?

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

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

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

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

Decimal Notation

x = 1.16030 \dots

Solution steps

ln (lo g_{x} (3)) = 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}}}

lo g_{2} (x + 5) - lo g_{2} (x - 1) = 1

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

1 - 2 ln (x) = - 4

ln (x) + x = 0

lo g_{2} (10 x + 5) - lo g_{2} (5) = 5

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