单项式1/5a^x+1b^3与-8b^2x-1b3是同类项,求x的值.

Question

单项式1/5a^x+1b^3与-8b^2x-1b3是同类项,求x的值.

Answer 1

1/5a^x+1b^3与-8b^2x-1b3是同类项
1/5a^x+1b^3=-8b^2x-1b3
1/5a^(x+1)=-8b^(2x-1)
(x+1)lna-ln5=(2x-1)ln(-b)-ln(8)
xlna+lna-ln5=2xln(-b)-ln(-b)-ln(8)
xlna+lna-ln5=2xln(-b)-ln(-b)-ln(8)
x[lna-2ln(-b)]=ln5-ln8-lna-ln(-b)
x=[ln5-ln8-lna-ln(-b)]/[lna-2ln(-b)]