Question

Suppose log subscript a x equals 2, space log subscript a y equals 5, and log subscript a z equals short dash 3. Find the value of the following expression. log subscript a open parentheses fraction numerator x y cubed over denominator z squared end fraction close parentheses

Answer 1

The value of the logarithmic expression  $\log _a (\frac{x^3y}{z^4} )$ is 24.

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 the above $\log _ax = 3, x = a^3$

$\log _ay = 7, y = a^7$

Substituting x = $a^3$, y = $a^7$  and z = $a^{-2}$ into the log function$\log _a (\frac{x^3y}{z^4} )$  we will have;

$\log _a (\frac{x^3y}{z^4} )\\=\log _a (\frac{(a^3)^3 \times a^7}{(a^{-2})^4} )\\= \log _a (\frac{a^9 \times a^7}{a^-^8} )\\= \log _a (\frac{a^1^6}{a^-^8} )\\= \log _a (\frac{x^3y}{z^4} )\\= \log _a a^2^4\\= 24 \log _a a\\= 24 \times 1\\= 24$

Hence, the value of the logarithmic expression is 24

What is logarithmic expression?

• In an exponential equation, the variable is expressed as an exponent. An equation using the logarithm of an expression containing a variable is referred to as a logarithmic equation.
• Check to determine if you can write both sides of the equation as powers of the same number before you attempt to solve an exponential equation.

To learn more about logarithmic expression with the given link

brainly.com/question/24211708

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