Solve Where applicable find an exact answer first then appro

Solve. Where applicable, find an exact answer first, then approximate to the nearest thousandth. 3^x+1 = 2^5x-2 log(x + 3) = 1 m- logx logx - log(x - 2) = log 4

Solution

a) 3^(x+1) = 2^(5x -2)

Taking log on both sides:

ln3^(x+1) = ln2^(5x -2)

(x+1)ln3 = (5x -2)ln2

x( ln3 -5ln2) = -ln2 -ln3

x =- (ln2 +ln3)/(ln3 -5ln2)

= 0.756

b) log( x+3) = 1 - logx

log(x+3) +logx =1

log(x(x+3)) = 1

x(x+3) = 10

x^2 +3x -10=0

use quadratic root formula:

x= (-3 +/- sqrt(9 +4*10)/2

= (-3 +/- 7)/2

= -5 , 2

Solution : x = -5 , 2

c) logx -log(x-4) =log4

log(x/(x-4) = log4

equate the argument inside the log:

x/(x-4) = 4

x= 4x -16

-3x = -16

Solution : x= 16/3