Using logarithms with a base of 10 find the value of x which satisfies the equation:?

7(4^x) = 3(5^x)





I know how to do logarithms, however i'm not sure what to do when x is on both sides, as in this equation.


Working out appreciated, explanation not required but will help.|||Use the rules of logs (i) log(ab) = log(a) + log(b) (ii) log(a^b) = b*log(a)





7*(4^x) = 3*(5^x) ----%26gt; log[7*(4^x)] = log[3*(5^x)]





----%26gt; log(7) + log(4^x) = log(3) + log(5^x)





Can you take it from there using the second rule above?|||Given: 7(4^x) = 3(5^x)


Take log on both sides, we get:


log[7(4^x)] = log[3(5^x)]





Tip: log (a*b) = loga + logb


log(a/b) = loga - logb


loga^b = bloga





log7 + log(4^x) = log3 + log(5^x)


log7 + xlog4 = log3 + xlog5


x(log4 - log5) = log3 - log7


x = (log3 - log7) / (log4 - log5) = (0.4771213 - 0.8450980) / (0.6020600 - 0.6989700


= 0.3671767 / 0.0969100 = 3.79


answer: 3.79 (approx)