Question 118700
Find the value of x:
{{{Log[10](5)+Log[10](x) = 2}}} Apply the "product rule" for logarithms:
{{{Log[b](M)+Log[b](N) = Log[b](MN)}}} to get:
{{{Log[10](5x) = 2}}} Rewrite this in "exponential" form:{{{Log[b](x) = y}}} ---> {{{x = b^y}}} to get:
{{{10^2 = 5x}}} Divide both sides by 5:
{{{100/5 = x}}} so...
{{{x = 20}}}
Check:
{{{Log[10](5)+Log[10](20) = 0.69897+1.30103}}} = 2