Question 197093
Solve for x:
{{{Log[2](Log[4](x)) = 1}}}Recalling the definition of the logarithm of a number or expression ({{{Log[4](x)}}}):
"The logarithm of a number ({{{Log[4](x)}}}) is the power to which the base (2) must be raised to equal that number"
{{{Log[2](Log[4](x)) = 1}}} can thus be written:
{{{2^1 = Log[4](x)}}} or 
{{{Log[4](x) = 2}}} Applying the definition again...
{{{4^2 = x}}} so that...
{{{highlight(x = 16)}}}
Check:
{{{Log[2](Log[4](x)) = 1}}} Substitute {{{x = 4^2}}}
{{{Log[2](Log[4](4^2)) = 1}}} Apply the power rule:
{{{Log[2](2*Log[4](4)) = 1}}} But {{{Log[n](n) = 1}}}, so
{{{Log[2](2) = 1}}} Again, {{{Log[n](n) = 1}}} so...
{{{1 = 1}}}