Question

I need help with this math question

Answer 1

B. 5

Explanation:

Step 1: Rewrite the equation a bit

`(7^(3)/(4))/(7^(x)/(8))=\sqrt[8]{7}\\7^(3)/(4)^-^(x)/(8)=7^(1)/(8)`

Step 2: Place a logarithm base 7 on both sides

`7^(3)/(4)^-^(x)/(8)=7^(1)/(8)\\log_77^(3)/(4)^-^(x)/(8)=log_77^(1)/(8)\\((3)/(4)-(x)/(8))log_77=(1)/(8)log_77\\((3)/(4)-(x)/(8))1=(1)/(8)1\\(3)/(4)-(x)/(8)=(1)/(8)`

Step 3: Solve for x

`(3)/(4)-(x)/(8)=(1)/(8)\\(6)/(8)-(x)/(8)=(1)/(8)\\-(x)/(8)=-(5)/(8)\\(x)/(8)=(5)/(8)\\x=5`

Neat exponent question :)