Answer:
[tex]x=100[/tex]
[tex]y=10[/tex]
Step-by-step explanation:
we are given
[tex]log_1_0(\frac{x}{y})=1[/tex]
Firstly, we will get rid of log
so, we will take exponent over 10 on both sides
[tex]10^{log_1_0(\frac{x}{y})}=10^{1}[/tex]
now, we can simplify it
[tex]\frac{x}{y}=10[/tex]
now, we can solve for x
[tex]x=10y[/tex]
we are given
[tex]log_1_0(x^2y^3)=7[/tex]
Firstly, we will get rid of log
so, we will take exponent of 10 on both sides
[tex]10^{log_1_0(x^2y^3)}=10^7[/tex]
[tex]x^2y^3=10^7[/tex]
now, we can plug back x from first equation
[tex](10y)^2y^3=10^7[/tex]
now, we can solve for y
[tex]100y^5=10000000[/tex]
[tex]\frac{100y^5}{100}=\frac{10000000}{100}[/tex]
[tex]y^5=100000[/tex]
now, we can take radical 5
[tex]y=\sqrt[5]{100000}[/tex]
[tex]y=10[/tex]
now, we can find x
[tex]x=10\times 10[/tex]
[tex]x=100[/tex]
So, solution is
[tex]x=100[/tex]
[tex]y=10[/tex]
