Question

How do you solve this

Answer 1

• domain: all terms are defined for all real numbers
• solution: x = 6

Explanation:

Rewrite the equation as a single exponential. After taking the log, the solution becomes obvious.

`5^(x-2)-7^(x-3)=7^(x-5)+11\cdot 5^(x-4)\\\\5^(x-2)-11\cdot 5^(x-4)=7^(x-3)+7^(x-5)\\\\5^(x-2)(1-11\cdot 5^(-2))=7^(x-3)(1+7^(-2))\\\\5^(x-2)(14)/(25)=7^(x-3)(50)/(49)\\\\1=(2\cdot 7^(x-3)5^4)/(2\cdot 5^(x-2)7^3)=\left((7)/(5)\right)^(x-6)\\\\0=(x-6)\log(1.4)\\\\x=6`