Question

5 ^(x+4)-5^x=100 how can we solve this

Answer 1

`5^(x+4)-5^x=100\\\\5^x\cdot5^4-5^x=100\\\\5^x(5^4-1)=100\\\\5^x(625-1)=100\\\\624\cdot5^x=100\ \ \ \ |:624\\\\5^x=(100)/(624)\\\\5^x=(25)/(156)\ \ \ \ |\log_5\\\\\log_55^x=\log_5(25)/(156)\\\\x=\log_525-\log_5156\\\\\boxed{x=2-\log_5156}\\\\\text{Used:}\\\\\log_ab^n=n\log_ab\\\\\log_aa=1\\\\\log_a(b)/(c)=\log_ab-\log_ac`