logarithms?

Question

1)
ln x + ln (x-5) = ln 4x

x=??

2)

2^2x+4=3^x-34



please show work

Answer 1

1. ln x(x-5) = ln 4x
x(x-5) = 4x
x^2-5x = 4x
x^2 = 9x
x = 9

2. Assuming 2^(2x+4)=3^(x-34)
log 2^(2x+4) = log 3^(x-34)
(2x+4) log 2 = (x-34) log 3
2xlog 2+4log 2 = xlog 3-34log 3
2xlog 2 - xlog 3 = -34log 3 - 4log 2
x = (-34log 3 - 4log 2)/(2log 2 - log 3) = -139.48

Answer 2

lnX + ln(X-5)=ln4X
implies that x*(X-5)=4X
therefore x*(x-5)-x*4=x*(x-9)=0
Therefore x=0 or x=9

The second problem has several different possible
interpretations.
I will assume that the left side of the equation is raising the
number 2 to the power (2x+4)
I will assume that the right side of the equation is raising the
number 3 to the power(x-34)
With these assumptions the first step is to take the log of each side of the equation.

.3010*(2X+4)-.4771*(3X-34)=0

.8293*X=17.4262
X=21.013