Question 375439
{{{2*Log[2](x)-Log[2](10) = 3*Log[2](4)}}} Use the power rule ({{{m*Log[b](x) = Log[b](x^m)}}}) to simplify.
{{{Log[2](x^2)-Log[2](10) = Log[2](4^3)}}} Add {{{Log[2](10)}}} to both sides.
{{{Log[2](x^2) = Log[2](4^3)+Log[2](10)}}} Simplify.
{{{Log[2](x^2) = Log[2](64)+Log[2](10)}}} Now apply the product rule ({{{Log[b](M)+Log[b](N) = Log[b](MN)}}}) the right side.
{{{Log[2](x^2) = Log[2](64*10)}}} Simplify.
{{{Log[2](x^2) = Log[2](640)}}} Apply the identity rule...If{{{Log[b](M) = Log[b](N)}}} then {{{M = N}}}
{{{x^2 = 640}}} Take the square root of both sides.
{{{highlight(x = 25.29822)}}} Approx.