SOLUTION: Solve each equation for x thus expressing x as a log function of y a) y = 3.5(2.7)^x b) y = 2.75(2/3)^x Can you please help me out ? Thanks so much in advance:)

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Solve each equation for x thus expressing x as a log function of y a) y = 3.5(2.7)^x b) y = 2.75(2/3)^x Can you please help me out ? Thanks so much in advance:)      Log On


   

Question 864887: Solve each equation for x thus expressing x as a log function of y
a) y = 3.5(2.7)^x
b) y = 2.75(2/3)^x
Can you please help me out ? Thanks so much in advance:)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first one to get you started


y+=+3.5%282.7%29%5Ex


y%2F3.5+=+%282.7%29%5Ex Divide both sides by 3.5.


log%28%28y%2F3.5%29%29+=+log%28%28%282.7%29%5Ex%29%29 Take the log of both sides (log can be any base, but I'm using base 10)


log%28%28y%2F3.5%29%29+=+x%2Alog%28%282.7%29%29 Pull down the exponent.


log%28%28y%2F3.5%29%29%2Flog%28%282.7%29%29+=+x Divide both sides by log%28%282.7%29%29 to isolate x. Note: for some reason, there's this weird gap, so ignore it and pretend it's not there.


x+=+log%28%28y%2F3.5%29%29%2Flog%28%282.7%29%29

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So we go from y+=+3.5%282.7%29%5Ex to x+=+log%28%28y%2F3.5%29%29%2Flog%28%282.7%29%29 after solving for x.