Logarithyms with Trigonometry 3

Geometry Level 2

If $\log_{\sin x } \cos x = \frac{1}{2}$ with $0 < x < \frac{ \pi } { 2}$ , what is the value of $\sin x$ ?

(-1+√5)/2 (-1-√2)/2 (2+√5)/2 (Golden Ratio)/2

1 solution

Christian Daang
Oct 24, 2014

log (cos x) base (sin x) = 1/2 -------> (sin x)^(1/2) = cos x

------> √(sin x) = cos x

------> sin x = (cos^2) x

------> sin x = 1 - (sin^2)x

------> (sin^2)x + (sin x) - 1 = 0

represent: X = sin x

-------> X^2 + X - 1 = 0

-------> X = (-1+√5)/2

-------> X = (sin x) = (-1+√5)/2

Final Answer: (-1+√5)/2

Christian, the dispute to your problem stated "Please state your problem clearly. If it's not possible for you to use latex..please try to put up a picture as it helps to understand better."

I agree that it is hard to understand what you are trying to say. IE is log X base Y equal to $\log_X Y$ or $\log_Y X$ ?

Calvin Lin Staff - 6 years, 7 months ago

I see,,, XD

1 log (cos x) base (sin x) = 1 log (cos x) [base (sin x)] .

Christian Daang - 6 years, 7 months ago

I've updated the question. Can you please check if this is what you intended?

Calvin Lin Staff - 6 years, 7 months ago

@Calvin Lin – yes it is. :D

Christian Daang - 6 years, 7 months ago

Also can you verify that you are receiving email from us? That is how we communicate with you about what the dispute states.

Calvin Lin Staff - 6 years, 7 months ago

Logarithyms with Trigonometry 3

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