Question 88611
You can use logarithms to solve exponential equations.
{{{10^(1-x) = 6^x}}} Take the commom logarthim of both sides.
{{{Log[10](10^((1-x))) = Log[10](6^x)}}} Apply the power rule for logarithms.
{{{(1-x)Log[10](10) = x*Log[10](6)}}} Recall that {{{Log[10](10) = 1}}}
{{{(1-x) = x*Log[10](6)}}} Add x to both sides.
{{{1 = x+xLog[10](6)}}} Factor out the x.
{{{1 = x(1+Log[10](6))}}} Divide both sides by {{{1+Log[10](6)}}}
{{{1/(1+Log[10](6)) = x}}} Evaluate this.
{{{1/(1+0.778) = x}}}
{{{x = 1/1.778}}}
{{{x = 0.56243}}}