Question 536640
Some general rules are
{{{ log(a) + log(b) = log(a*b) }}}
{{{ log(a) - log(b) = log(a/b) }}}
{{{ log(a^b) = b*log(a) }}}
You can use the rules in both directions
{{{ log(7,x+1)=log(7,2x^2 - x - 3) }}}
The rule to apply here is:
If this is true: {{{ log(a,b) = log(a,c) }}},
then {{{ b = c }}}, so
{{{ x + 1 = 2x^2 - x - 3 }}}
{{{ x + 1 = (2x - 3)*(x + 1) }}} (I used trial and error)
Divide both sides by {{{ x + 1 }}}
{{{ 1 = 2x - 3 }}}
{{{ 2x = 4 }}}
{{{ x = 2 }}}
check answer:
{{{ log(7,2+1)=log(7,2*2^2 - 2 - 3) }}}
{{{ log(7,3) = log(7, 8 - 2 - 3) }}}
{{{ log(7,3) = log(7, 3) }}}
OK