Let 2^a = 5 and 2^b = 7. Using exponent rules, solve the equation in terms of a and b.

Question

0.4^x = 343

Answer 1

0.4^x = 343
(2/5)^x = 343
log both sides, with base 2

log₂(2/5)^x =log₂ 343 = log₂ 7^3
x(log₂ 2 - log₂ 5) = 3log7 ------- #1

now 2^a = 5 ---> log₂5 = a
and 2^b = 7 ---> log₂7 = b

back in #1
x(log₂2 - log₂5 = 3log₂7
x(1 - a) = 3b

x = 3b/(1-a)