SOLUTION: please help me, im so confused! Solve 5^(sin2x) = 3.307 if i wasnt clear sin2x is the exponent of 5. we're learning about logarithms and natural logs and stuff, i just dont g

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Question 35303: please help me, im so confused!
Solve 5^(sin2x) = 3.307
if i wasnt clear sin2x is the exponent of 5. we're learning about logarithms and natural logs and stuff, i just dont get it!
Answer by longjonsilver(2297) (Show Source):
You can put this solution on YOUR website!
if you are just learning about logs etc, this is a nasty question to give you.

Take logs to base5: i shall just write the word "log" without a subscript.

Now, the reason for taking logs to base 5 is that log to base 5 of (5) is 1. So:

Now, what the hell is log-base5 of (3.307)...your calculator doesn't store base5 logs. It does store base10 though, so we are going to convert the base5 into a base10. Pretty straightforward really:

--> here the 2 logs are now both base10. Work the right hand side out on your calculator to give:

sin2x = 0.743142 to 6dp

so, now need to solve this trig equation. What is the domain of x? Since sin is a repeating function, you will have an infinite number of solutions, as it stands.

I shall do the "obvious" one:
2x = sin^(-1)(0.743142)
2x = whatever
x = whatever/2

--> i do not have a calculator handy to find this angle for you.

jon.