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drek232000

United States
Joined: Nov 22, 2010
Posts: 1
Status: Offline

 Propertiesof exponential and Logarithmic Functions Reply to this Post Reply with Quote

Ok so the quarter is winding down and these questions are getting much harder. I have been really struggling on these couple of questions and would love to see if anyone here can help me.

Simplify the following expressions (reduce to a single expnential or a single logarithm)

1. 2^3x+1*4^1-x/4
8^x^2-1

2. log3(x+1)-2log3(x-1)+log3(x^2+x-2)

Anyone that could help out even just a little bit would be of great help thank you.
 [Nov 22, 2010 9:07:17 PM] [Link]
pskinner

Joined: Apr 2, 2005
Posts: 797
Status: Offline
 Re: Propertiesof exponential and Logarithmic Functions Reply to this Post Reply with Quote

 Ok so the quarter is winding down and these questions are getting much harder. I have been really struggling on these couple of questions and would love to see if anyone here can help me. Simplify the following expressions (reduce to a single expnential or a single logarithm)1. 2^3x+1*4^1-x/4 8^x^2-12. log3(x+1)-2log3(x-1)+log3(x^2+x-2)Anyone that could help out even just a little bit would be of great help thank you.

For #1, I assume you mean

2^(3x+1)*4^(1-x/4)
8^(x^2-1)

With that in mind, rewrite 4^(1-x/4)=2^2^(1-x/4)=2^(2-x/2)

and rewrite 8^(x^2-1)=2^3^(x^2-1)=2^(3x^2-3)

Once you have each of the three terms with the same base, you can combine exponents, recalling that moving 2^(3x^2-3) from the denominator to the numerator yields the negative of the exponent: 2^(3-3x^2) and then you just add the exponents and get 2^(sum of the exponents)

For #2, rewrite 2log(3(x-1) as log[(3^2)(x-1)^2]

log3(x+1)-2log3(x-1)+log3(x^2+x-2)

=log[3(x+1)*3(x^2-2)/{(3^2)(x-1)^2)}]
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Principal Skinner
 [Nov 23, 2010 9:20:19 AM] [Link]