Question

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

Answer 1

ANSWER

x=100,y=10

EXPLANATION

The given logarithmic equations are;

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

This implies that,

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

and

$log_{10}( \frac{x}{y} ) = 1$

This implies that,

$\frac{x}{y} = {10}^{1}$

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

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

$x = 10(10) = 100$