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How can we simplify this expression below into a single logarithm? 3log(x)+1/2log(4y)−log(z)

Sagot :

aklee18oo

Answer:

[tex]log(\frac{2x^3\sqrt{y} }{z} )[/tex]

Step-by-step explanation:

We can start by using the power property of logarithms to rewrite the expression. We raise the contents of the logarithm to the power of the coefficient:

[tex]log(x^3) + log([4y]^\frac{1}{2} )-log(z)\\log(x^3) + log(2\sqrt{y})-log(z)[/tex]

Now, we can use both the addition and subtraction properties of logarithms to rewrite the expression. Addition becomes multiplication while subtraction becomes division:

[tex]log(\frac{x^3*2\sqrt{y}}{z} )[/tex]

And to write it in a more proper way:

[tex]log(\frac{2x^3\sqrt{y} }{z} )[/tex]

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