Explain graph of function & solve logarthmic functions Need help ASAP, this is due tomorrow!!!!!!?

Question

Two problems:

1. I have NO idea how to do this and its not in my book

Explain how to use the graph of f(x)= (3/4)^x to produce the graph of 3/4(x) +2

2. This one I got down to where I have to factor and I cant factor 5x^2 + 75x -10 .... I think I went wrong somewhere???

Solve: log 5x + log (x + 15) = 1

Answer 1

f(x)= (3/4)^x
log(f(x))= xlog(3/4)
is as close as I can come without more information

The slope of (3/4)^x is
(ln(3/4))(3/4)^x
Try
2 + x(ln(3/4))(3/4)^x = (3/4)^x

5x^2 + 75x - 10 =
5(x^2 + 15x - 2) =
5(x^2 + 15x + (15/2)^2 - (15/2)^2 - 2) =
5(x + 15/2)^2 - 225/4 - 2) =
5(x + 15/2)^2 - (225 + 8)/4) =
5(x + 15/2)^2 - 233/4) =
5(x + 15/2 - (1/2)√233)(x + 15/2 + (1/2)√233)

log 5x + log (x + 15) = 1
5x^2 + 75x = 10
x^2 + 15x = 2
x = - (1/2)(15 + √233), - (1/2)(15 - √233)

Answer 2

y= (3/4)^x + 2 is the same as (3/4)^x except that is lifted 2 units up in the y-axis, so the y-intercept is increased by 2. the x-intercept changes as well u need 2 c hw it does from ur gaph
2: it can be factorised but i am sure u may hav had a problem wiz da signs b4
log 4x + log (x+15) = log e
log (4x*(x+15))= log e
4x^2 + 60 x - e = 0

Answer 3

log 5x + log (x + 15) = 1
log[(5x)(x+15)] = 1
5x^2+75x=10
5x^2 + 75x - 10 = 0

divide by 5 throughout
x^2 + 15x - 2 = 0

use quadratic solution
x = [ -15 ± Sq Root ( 233 ) ] / 2