step 1 is the equation.
step 2 divides both sides of the equation by 1.7
step 3 divides both sides of the equation by 4.6^x.
step 4 takes the log of both sides of the equation.
step 5 converts log(a/b) to log(a) - log(b).
step 6 converts log(a^x) to x*log(a).
step 7 factors out the x on the left side of the equation.
step 8 divides both sides of the equation by (4log(2.8)-log(4.6)).
step 9 solves for x.
the answer is an irrational number and so can't be converted to a fraction.
if you need to have everything in fraction form, then go back to step 8 and convert 1.7 and 2.8 and 4.6 to a fraction.
you will get:
log(70/17)
x = -----------------------------
4*log(14/5) - log(23/5)