Question

If log10(x^{2}y^{3})=7 and log10 (x/y)=1 , then x=__ and y= __

Answer 1

Answer:

$x=100$

$y=10$

Step-by-step explanation:

we are given

$log_1_0(\frac{x}{y})=1$

Firstly, we will get rid of log

so, we will take exponent over 10 on both sides

$10^{log_1_0(\frac{x}{y})}=10^{1}$

now, we can simplify it

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

now, we can solve for x

$x=10y$

we are given

$log_1_0(x^2y^3)=7$

Firstly, we will get rid of log

so, we will take exponent of 10 on both sides

$10^{log_1_0(x^2y^3)}=10^7$

$x^2y^3=10^7$

now, we can plug back x from first equation

$(10y)^2y^3=10^7$

now, we can solve for y

$100y^5=10000000$

$\frac{100y^5}{100}=\frac{10000000}{100}$

$y^5=100000$

now, we can take radical 5

$y=\sqrt[5]{100000}$

$y=10$

now, we can find x

$x=10\times 10$

$x=100$

So, solution is

$x=100$

$y=10$