Question 456439
Take the log of both sides
{{{ log(1.72^x) = log(32) }}}
{{{ log(1.72^x) = log(2^5) }}}
Use the rule {{{ log(a^b) = b*log(a) }}}
{{{ x*log(1.72) = 5*log(2) }}}
{{{ x = (5*log(2)) / log(1.72) }}}
{{{ x = (5* .3010) / .2355 }}}
{{{ x = 1.5050/.2355 }}}
{{{ x = 6.391 }}}
check answer:
{{{ 1.72^x= 32 }}}
{{{ 1.72^6.391 = 32 }}}
{{{ 32.008 = 32 }}}
close enough