What is the answer to ln(x)=4log_{x}(e) ?

The answer to ln(x)=4log_{x}(e) is x=e^2,x= 1/(e^2)

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ln(x)=4log_{x}(e)

ln (x) = 4 lo g_{x} (e)

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

Decimal Notation

x = 7.38905 \dots, x = 0.13533 \dots

Solution steps

ln (x) = 4 lo g_{x} (e)

Apply log rules

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

Rewrite the equation with

ln (x) = u

u = \frac{4}{u}

Solve

u = \frac{4}{u} : u = 2, u = - 2

u = 2, u = - 2

Substitute back

u = ln (x),

solve for

x

Solve

ln (x) = 2 : x = e^{2}

Solve

ln (x) = - 2 : x = \frac{1}{e ^{2}}

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

Verify Solutions:

x = e^{2}

True

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

True

The solutions are

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

lo g_{9} (4) = 2 lo g_{9} (x)

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

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

5 ln (8 x - 5) - 20 = 5

lo g_{10} (3 x - 1) = 2

What is the answer to ln(x)=4log_{x}(e) ?
The answer to ln(x)=4log_{x}(e) is x=e^2,x= 1/(e^2)