What is the value of x when 4 to the x equals 3 to the x plus 2 power?

Answer 1

4x = 3(x+2)

x log(4) = (x+2) log(3)

log(4) = 0.60206
log(3) = 0.4771213

0.60206 x = 0.4771213 (x+2)

0.60206 x = 0.4771213 x + 0.9542425

0.1249387 x = 0.9542425

x = 0.9642425 / 0.1249387 = 7.7177248

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Check:

4(7.7177248) = 44,313

3(9.7177248) = 43,304

I think the check is good, even though the numbers differ by about 2.3%. My gut feeling is that with the
inaccuracies introduced in the log and exponentiation process, this is probably as good as you'll get.