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July 17th, 2012, 09:21 AM   #1
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Exponential/logarithmic equations

Can I get help with
c. 3(4)^3x-2=192
d. 1/3logx=1
e. log2(x+3)+log2(x-3)=4
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July 17th, 2012, 09:42 AM   #2
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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.
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July 17th, 2012, 10:08 AM   #3
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Re: Exponential/logarithmic equations

Thank you so much!
Can you also post a clear explanation of why
1/3log2(- has a real solution?
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July 17th, 2012, 10:11 AM   #4
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Re: Exponential/logarithmic equations

^im so if it does or does not have a clear solution.
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July 17th, 2012, 10:55 AM   #5
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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.
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July 17th, 2012, 11:22 AM   #6
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Re: Exponential/logarithmic equations

Thanks a lot! You really help!
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July 17th, 2012, 11:24 AM   #7
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Re: Exponential/logarithmic equations

























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July 18th, 2012, 09:18 PM   #8
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Re: Exponential/logarithmic equations

cos^2x 1+sinx
1+2sinx-3sin^2x = 1+3sinx

solve the trig identity please! with steps shown.
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July 18th, 2012, 09:30 PM   #9
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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.
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July 18th, 2012, 09:39 PM   #10
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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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