How can logarithms help solve an equation involving trigonometric functions?

[Petkovsky]

4^{sinx} = \sqrt[cosx]{2}

I use logarithmic and i get :

sinx * log(4) = (1/cosx) * log(2)

sinx*cosx = log(2)/log(4)


what should i do next?

 

[Tedjn]

What is log(2)/log(4)? Try applying a change of base rule. Afterward, see if you can use any of your trigonometric formulas to simplify.

 

[kamerling]

4^{sinx} = \sqrt[cosx]{2}

I use logarithmic and i get :

sinx * log(4) = (1/cosx) * log(2)

sinx*cosx = log(2)/log(4)


what should i do next?

What is log(2)/log(4) ?

 

[Petkovsky]

Thank you, i solved it