How do you solve 2 log x = log 64?
\(x>0 \\ \\
2 \log x= \log 64 \\
\log x^2=\log 64 \\
x^2=64 \\
x=-8 \ \lor \ x=8 \ and \ x>0 \\
\boxed{x=8}\)
Used formulas:
\(n \log_a b=\log_a b^n \\
\log_a b, b>0\)
\(2\log { x } =\log { 64 } \\ \\ \log { \left( { x }^{ 2 } \right) } =\log { \left( { 8 }^{ 2 } \right) } \\ \\ { x }^{ 2 }={ 8 }^{ 2 }\\ \\ x={ \left( { 8 }^{ 2 } \right) }^{ \frac { 1 }{ 2 } }\\ \\ x=8\)