Question

5. I need help with question in the attached picture!

Answer 1

x=100,y=10

Step-by-step explanation

The given logarithmic equations are;

`log_(10)( {x}^(2) {y}^(3) ) = 7`

This implies that,

`{x}^(2) {y}^(3) = {10}^(7) ...(1)`

and

`log_(10)( (x)/(y) ) = 1`

This implies that,

`(x)/(y) = {10}^(1)`

`x = 10y...(2)`

Put equation (2) into equation (1)

`{(10y)}^(2) {y}^(3) = {10}^(7)`

`10 ^(2) y^(2) {y}^(3) = {10}^(7)`

`{y}^(5) = {10}^(5)`

Hence y=10.

This implies

`x = 10(10) = 100`