Question 80419
Solve for x:
{{{(1/7)^x = 49}}} But {{{49 = 7^2}}} = {{{1/7^(-2) = (1/7)^-2}}}, so we get:
{{{(1/7)^x = (1/7)^-2}}}, therefore x = -2

If you are not comfortable with this approach, here's another one:
{{{(1/7)^x = 49}}} Take the logarithm of both sides.
{{{Log[10](1/7)^x = Log[10](49)}}} Apply the power rule to the left side.
{{{x*Log[10](1/7) = Log[10](49)}}} Divide both sides by {{{Log[10](1/7)}}}
{{{x = (Log[10](49))/Log[10](1/7)}}} Do this with your calculator.
{{{x = -2}}}