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July 17th, 2012, 09:21 AM  #1 
Newbie Joined: Jul 2012 Posts: 18 Thanks: 0  Exponential/logarithmic equations
Can I get help with c. 3(4)^3x2=192 d. 1/3logx=1 e. log2(x+3)+log2(x3)=4 
July 17th, 2012, 09:42 AM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  Re: Exponential/logarithmic equations
I have split your post into its own topic. c) Divide through by 3: Equate exponents: Now solve for x... d) Multiply through by 3 Convert from logarithmic to exponential form: e) Observe, we require . Use additive property of logs: Convert from logarithmic to exponential form: Solve for x, and discard any roots less than or equal to 3. 
July 17th, 2012, 10:08 AM  #3 
Newbie Joined: Jul 2012 Posts: 18 Thanks: 0  Re: Exponential/logarithmic equations
Thank you so much! Can you also post a clear explanation of why 1/3log2( has a real solution? 
July 17th, 2012, 10:11 AM  #4 
Newbie Joined: Jul 2012 Posts: 18 Thanks: 0  Re: Exponential/logarithmic equations
^im so if it does or does not have a clear solution.

July 17th, 2012, 10:55 AM  #5 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  Re: Exponential/logarithmic equations
A logarithm of a negative value does not have a real solution, it will be a complex value. This is because (in the case of the given expression) is positive for all real values of x.

July 17th, 2012, 11:22 AM  #6 
Newbie Joined: Jul 2012 Posts: 18 Thanks: 0  Re: Exponential/logarithmic equations
Thanks a lot! You really help!

July 17th, 2012, 11:24 AM  #7 
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: Exponential/logarithmic equations 
July 18th, 2012, 09:18 PM  #8 
Newbie Joined: Jul 2012 Posts: 18 Thanks: 0  Re: Exponential/logarithmic equations
cos^2x 1+sinx 1+2sinx3sin^2x = 1+3sinx solve the trig identity please! with steps shown. 
July 18th, 2012, 09:30 PM  #9 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  Re: Exponential/logarithmic equations
Could you more clearly state the identity you wish to prove? I could venture some guesses, but I think it would be better for you to clearly state the problem.

July 18th, 2012, 09:39 PM  #10 
Newbie Joined: Jul 2012 Posts: 18 Thanks: 0  Re: Exponential/logarithmic equations
sorry about that. https://www.desmos.com/calculator there is a link to the equation. Also, 8. Find the sine of the angle formed by two rays that start at the origin of the Cartesian plane if one ray passes through the point (3root3,3) and the other ray passes through the point(4,4root3) . Round your answer to the nearest hundredth in necessary. 

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