Question

What is the value of log(x exponent 2 y exponent 3 divided by z) when given the following:

log(x) = 3
log(y) = 2
log(z) = -1

A. 12
B. 13
C. 16
D. 18

Urgently need answer

Answer 1

B. 13

Step-by-step explanation:

`\sf\:Given\:expression: log((x^2 y^3)/(z) )`

Logarithm rules:

`\sf (i) \ \sf log(ab) = log(a) + log(b)\\ \\ (ii) \ log(a/b) = log(a) - log(b)\\\\ (iii) \ log(a^n) = n log(a)`

Breakdown of the expression:

`\rightarrow \sf log\left((x^2y^3)/(z)\right)`

`\rightarrow \sf log\left(x^2\right) + log\left(y^3\right) - log(z)`

`\rightarrow \sf 2\log\left(x\right)+3\log \left(y\right)-\log \left(z\right)`

insert given values

`\rightarrow \sf 2(3)+3(2)-(-1)`

`\rightarrow \sf 13`