Use the product property of logarithms, .

Multiply by by adding the exponents.

Multiply by .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

The exponent of a factor inside a logarithm can be expanded to the front of the expression using the third law of logarithms. The third law of logarithms states that the logarithm of a power of is equal to the exponent of that power times the logarithm of .

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

To solve for , rewrite the equation using properties of logarithms.

Exponentiation and log are inverse functions.

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

Solve for x natural log of x+ natural log of x^2=5