Question

Suppose log subscript a x equals 3, log subscript a y equals 7, and log subscript a z equals short dash 2. Find the value of the following expression. log subscript a open parentheses fraction numerator x cubed y over denominator z to the power of 4 end fraction close parentheses

Answer 1

Answer:

24

Step-by-step explanation:

Given the following logarithmic expressions $log_ax = 3, log_ay = 7, log_az = -2$, we are to find the value of $log_a(\frac{x^3y}{z^4} )$

$from\ log_ax = 3, x = a^3\\\\from\ log_ay = 7,y = a^7\\\\from\ log_az = -2, z = a^{-2}$Substituting x = a³, y = a⁷ and z = a⁻² into the log function $log_a(\frac{x^3y}{z^4} )$ we will have;

$= log_a(\frac{x^3y}{z^4} )\\\\= log_a(\dfrac{(a^3)^3*a^7}{(a^{-2})^4} )\\\\= log_a(\dfrac{a^9*a^7}{a^{-8}} )\\\\= log_a\dfrac{a^{16}}{a^{-8}} \\\\= log_aa^{16+8}\\\\= log_aa^{24}\\\\= 24log_aa\\\\= 24* 1\\\\= 24$

Hence, the value of the logarithm expression is 24