here we're asked to solve a exponential equation. The first step is to use the one-to-one
property of logarithmic functions and
take the log of both sides now you can
choose any base you want but since the
calculator has a base 10 log button and
a base e log button you should choose
one of those I'm going to choose to take
the common log log base 10 of both sides
when you take log base 10 of both sides
in this case the right side log of 10 is
simply 1 so that works out nicely now
the second step is to apply the property
of the log that says exponents can be
written as coefficients so here I'm
going to rewrite this as x times log of
2 now like I said log of 10 is just one
okay once you write it in that way the
exponent as an X a coefficient you can
then isolate that exponent here by
simply dividing both sides by log of 2
okay on the right on the left side here
those cancel and you're left with x
equals 1 over log of 2 so that's the
exact answer now you might be asked to
write an approximate answer in which
case you would just do that on a
calculator and 1 / log of 2 comes out to
about three point three two one nine if
I round that off to four places
