help with a homework question about logarithms

[u/earlgray060708]

I can't seem to understand this one problem. could somebody help me solve for X?

(lnx)^3-ln(x^25)=0

[u/GirlWhoCriedSuprnova]

Consider that ln(x²⁵ ) = 25*(lnx).

[u/GirlWhoCriedSuprnova → u/[deleted]]

I agree! Good job

[u/Uli_Minati]

Here are the concepts you'll need:

Logarithm of a Power https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:log-prop/v/logarithm-of-a-power

Factorization with Substitution https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-factor/x2ec2f6f830c9fb89:factor-w-structure/v/factor-w-substitution

Zero Product Property https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:factored-form-quadratics/v/zero-product-property

[u/Hampster-cat]

Along with other suggestions, let u = ln(x). Now you have an easy-to-factor polynomial. Just don't forget that the solutions to the polynomial are NOT the solutions to the original problem.