What is the answer to 5ln^2(x)=25ln(x^2) ?

The answer to 5ln^2(x)=25ln(x^2) is x=e^{10},x=1

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5ln^2(x)=25ln(x^2)

5 ln^{2} (x) = 25 ln (x^{2})

x = e^{10}, x = 1

Decimal Notation

x = 22026.46579 \dots, x = 1

Solution steps

5 ln^{2} (x) = 25 ln (x^{2})

Divide both sides by

5

\frac{5 ln ^{2} ( x )}{5} = \frac{25 ln ( x ^{2} )}{5}

Simplify

ln^{2} (x) = 5 ln (x^{2})

Apply log rules

ln^{2} (x) = 5 \cdot 2 ln (x)

Rewrite the equation with

ln (x) = u

u^{2} = 5 \cdot 2 u

Solve

u^{2} = 5 \cdot 2 u : u = 10, u = 0

u = 10, u = 0

Substitute back

u = ln (x),

solve for

x

Solve

ln (x) = 10 : x = e^{10}

Solve

ln (x) = 0 : x = 1

x = e^{10}, x = 1

Verify Solutions:

x = e^{10}

True

, x = 1

True

The solutions are

x = e^{10}, x = 1

4 lo g_{2} (x) = 3

lo g_{5} (4 x + 7) - lo g_{5} (x) = 2

lo g_{10} (y) = (- 0.05085)

lo g_{2} ((r + 8)^{2}) = 4

8 lo g_{10} (n) - n = 0

What is the answer to 5ln^2(x)=25ln(x^2) ?
The answer to 5ln^2(x)=25ln(x^2) is x=e^{10},x=1
Solve for x: 5ln^2(x)=25ln(x^2)
The solution is x=e^{10},x=1