Question

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

Answer 1

`log((2x^3√(y) )/(z) )`

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]^(1)/(2) )-log(z)\\log(x^3) + log(2√(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((x^3*2√(y))/(z) )`

And to write it in a more proper way:

`log((2x^3√(y) )/(z) )`