Question

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

Answer 1

Answer:

$log(\frac{2x^3\sqrt{y} }{z} )$

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:

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

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

$log(\frac{x^3*2\sqrt{y}}{z} )$

And to write it in a more proper way:

$log(\frac{2x^3\sqrt{y} }{z} )$