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

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.
RELATED QUESTIONS
Please help me solve {{{5-sin2x=7sin2x}}} in... (answered by Alan3354)

Solve 5^sin2x = 3.307 (answered by josmiceli)

this is trig identities, if you could please help me prove the following identity true (answered by Fombitz)

Hello (again), Please disregard the first question sent to you from... (answered by vleith)

Determine the values of sin2x, cos2x, and tan2x: Sinx=3/5, and x is acute (answered by Edwin McCravy)

Please help me solve this equation:... (answered by Alan3354)

Please help me solve this equation: {{{ cosx=sin2x... (answered by lwsshak3)

Arrange the steps in the correct order to solve this trigonometric equation.... (answered by Solver92311,ikleyn)

I am in algebra 2 and we are learning about "interperetting graphs. Equations like, "If... (answered by scott8148)