SOLUTION: i really need help on these problems.. thank you :) describe how the graph of the function is related to the graph of its parent function. y = 3^x-4 Write the logarith

Algebra ->  Algebra  -> Exponential-and-logarithmic-functions -> SOLUTION: i really need help on these problems.. thank you :) describe how the graph of the function is related to the graph of its parent function. y = 3^x-4 Write the logarith      Log On

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Question 186664: i really need help on these problems.. thank you :)
describe how the graph of the function is related to the graph of its parent function.
y = 3^x-4
Write the logarithmic expression as a single logarithm.
log a - log ab
expand the logarithm
log y^2/z
write the experssion as a single natural log
5 ln a + 3 ln b
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first two to get you going in the right direction.

# 1



I'm assuming that the equation is y=3%5Ex-4.


The parent function is y=3%5Ex which looks like


+drawing%28500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0A+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C3%5Ex%29%0D%0A%0D%0A%29 Graph of y=3%5Ex



and the function y=3%5Ex-4 is simply the parent function shifted down 4 units like this


+drawing%28500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0A+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C3%5Ex%2C3%5Ex-4%29%0D%0A%0D%0A%29 Graph of y=3%5Ex (red) and y=3%5Ex-4 (green)





# 2

log%2810%2C%28a%29%29-log%2810%2C%28ab%29%29 Start with the given expression.


log%2810%2C%28a%2F%28ab%29%29%29 Combine the logs using the identity log%28b%2C%28A%29%29-log%28b%2C%28B%29%29=log%28b%2C%28A%2FB%29%29


log%2810%2C%28cross%28a%29%2F%28cross%28a%29%2Ab%29%29%29 Cancel out the common terms.


log%2810%2C%281%2Fb%29%29


So log%2810%2C%28a%29%29-log%2810%2C%28ab%29%29=log%2810%2C%281%2Fb%29%29 where a%3E0 and b%3E0