Question

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

Answer 1

Hi,

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