Simplify the left side.
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 by and simplify.
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.
Solve for x natural log of x+ natural log of x^2=5