Question

11^-x+3=5^-3x. solve for x write the exact answer using base -10 logarithms

Answer 1

Hi,

$11^{-x+3}=5^{-3x}\\ (-x+3) log 11 = -3x log 5\\ -x*log 11 + 3x* log 11 =-3*log 11\\ x(-log 11 +3 log 5)=-3 log 11\\ x=\dfrac{-3 log 11}{(3 log 5 -log 11} \\ x=-2.959854....$