Verified answer

I am sure this will help!! :-)

Hi,

For your case, you'll only need to change the base on the first part of the equation. I'll use base 10 as it's built-in to a calculator and fairly easy to understand.

To change bases (from a to b), you use the following formula:

log(base a)x = log(base b)x / log(base b)a.

So for your specific example, you have:

log(base 3)24 = log(base 10)24 / log(base 10)3

= 1.3802 / 0.4771

= 2.8929

For the second part, you don't need to change the base as:

log(base a)a = 1

So filling in the numbers:

log(base 3)24 - 3log(base 2)2

= 2.8929 - 3

= -0.1071

Hope that helps.

Rewrite as: Logb x^5 - Logb y^(1/4)+ Logb z^2 Use the rules to get: Logb (x^5/y^(1/4))*z^2) The addition signs correspond to multiplying and the subtraction signs correspond to division. You can check your answers on a calculator by substituting numbers such as x=3, y=5, and 7=z and 10 for b (you can use the LOG key on your calculator) or use (exponential) e and the LN key. You should get the same answers for both the original and simplified equation.

log(base 3)24 - 3 log(base 2)2 = log24/log3 - 3

since log (base 2) 2 = 1

change of base is:

log(base 3)24 = log24/log3

[log (base 3)24] - [3 log(base 2)2]

= [log (base 3)24] - 3

= [log (base 3)24] - [log (base 3)27]

= log (base 3) (24/27)

= log (base 3) (8/9)