Solve each equation log x log 3 log 52 log4 x2 7 log4 2

Solve each equation. log x - log 3 = log 52 log_4 (x^2 + 7) + log_4 2 = 2 log_3 3x^2 + log_3 4 = 5

1) logx - log3 = log52

use the log property: logA -logB = log(A/B)

log(x/3) = log52

x/3 = 52 ---> x = 156

3) log4(x^2 +7) +log4(2) = 2

use the log property: logA +logB = logA*B

log4(x^2+7)2 =2

2(x^2 +7) = 4^2

x^2 +7 = 16/2

x^2 = 8-7 =1

x = -1 , 1

5) log3(3x^2) +log3(4) =5

use the log property: logA +logB = logA*B

log3(3x^2*4) = 5

12x^2 = 3^5

x^2 = 243/12

x = sqrt(243/12) = sqrt(243/3*4)

= sqrt(81/4) = +/- 9/2

x = -9/2 , 9/2