Evaluating logarithmic expressions

Celeste wants to have her hair cut and permed and also go to lunch. she knows she will need $50. the perm cost twice as much as her haircut and she needs $5 for lunch. how much does the perm cost?

If cos(2x) = tan^2(y), show that cos(2y) = tan^2(x).

In an improper fraction, is the numerator equal to, less than, or greater than the denominator