Question 540870
Solve for x:
{{{g(x) = (1/5)^x}}} for {{{g(x) = sqrt(5)}}}
{{{(1/5)^x = sqrt(5)}}} Rewrite the left and right sides: {{{(1/5)^x = (5)^(-x)}}} and {{{sqrt(5) = (5)^(1/2)}}}
{{{(5^(-1))^x = (5)^(1/2)}}} Take the log of both sides.
{{{Log(5)^(-x) = Log(5)^(1/2)}}} Apply the "power rule".
{{{-x*Log(5) = (1/2)*Log(5)}}} Divide both sides by {{{Log(5)}}}
{{{-x = (1/2)(Log(5)/Log(5))}}} Simplify.
{{{-x = 1/2}}} Multiply by -1.
{{{highlight(x = -(1/2))}}}