How to solve Logarithms

1) 4log₃2 - 2log₃x = 1

Note that  1   =  log₃ 3  .....so we can write

4 log₃ 2 - 2log₃x  = log₃ 3      {  log property :  b log a  =  loga^b  }

log₃ 2^4  - log₃x^2  = log₃3   { log a - log b  =  log (a/b) }   ⇒ 2⁴  = 16

log₃ (16/ x^2)  = log₃ 3

Since  we have equal logs   we can just solve

16/x^2  =  3

x^2  = 16 / 3         take the positive root 

x  =  4 / √ 3   ≈ 2.3094

2) logx² = 2       ....we can write

2 log x  =  2         divide both sides by 2

log x  =  1

This says that    10^1  =  x  =  10