Question

Without exponents logc (xy^6z^-4) what is the equivalent expression

Answer 1

By eliminating exponents, the logarithmic expression $\log_{c} x\cdot y^{6}\cdot z^{-4}$ is equivalent to the logarithmic expression $\log_{c} x + 6\cdot \log_{c} y - 4\cdot \log_{c} z$.

How to simplify logarithmic functions

In this problem we are supposed to eliminate all exponents of a logarithmic function by applying any of the following properties:

1. ㏒ x · y = ㏒ x + ㏒ y
2. ㏒ x/y = ㏒ x - ㏒ y
3. ㏒ yˣ = x · ㏒ y

Now, we proceed to simplify the function:

$\log_{c} x\cdot y^{6}\cdot z^{-4}$

$\log_{c} x + \log_{c} y^{6} + \log_{c} z^{-4}$

$\log_{c} x + 6\cdot \log_{c} y - 4\cdot \log_{c} z$

By eliminating exponents, the logarithmic expression $\log_{c} x\cdot y^{6}\cdot z^{-4}$ is equivalent to the logarithmic expression $\log_{c} x + 6\cdot \log_{c} y - 4\cdot \log_{c} z$.

To learn more on logarithms: brainly.com/question/24211708

#SPJ1