Question

How do you solve 2 log x = log 64?

Answer 1

`2\log { x } =\log { 64 } \\ \\ \log { \left( { x }^( 2 ) \right) } =\log { \left( { 8 }^( 2 ) \right) } \\ \\ { x }^( 2 )={ 8 }^( 2 )\\ \\ x={ \left( { 8 }^( 2 ) \right) }^{ \frac { 1 }{ 2 } }\\ \\ x=8`

Answer 2

`x>0 \\ \\ 2 \log x= \log 64 \\ \log x^2=\log 64 \\ x^2=64 \\ x=-8 \ \lor \ x=8 \ and \ x>0 \\ \boxed{x=8}`

Used formulas:

`n \log_a b=\log_a b^n \\ \log_a b, b>0`