Question

2^(2x+11)=3^(x-12)


x=?

Answer 1

By taking the natural logarithm of both sides:

2^(2x + 11) = 3^(x - 2)
==> ln[2^(2x + 11)] = ln[3^(x - 2)]
==> (2x + 11)ln(2) = (x - 2)ln(3), since ln(a^b) = b*ln(a)
==> 2x*ln(2) + 11ln(2) = x*ln(3) - 2ln(3), by distributing
==> 2x*ln(2) - x*ln(3) = -2ln(3) - 11ln(3), by bringing all x terms to one side
==> x[2ln(2) - ln(3)] = -2ln(3) - 11ln(3), by factoring out x
==> x = -[2ln(3) + 11ln(3)]/[2ln(2) - ln(3)] ≈ -49.6449.