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

<h3>What is logarithmic expression?</h3>

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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1 year ago

Z+3=-6<br><br> z=??<br><br> i need help asap!

katrin2010 [14]

subtract 3 from both sides to isolate the variable

Z + 3 -3 = -6 -3

Z + 0 = -9

Z = -9

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