Calculus

[emilyroll0]

Given that log2 = a and log3 = b, evaluate each of the following in terms of a or b:

(a) log8

(b) log9

(c) log sqrt24

 

[Denis]

Did you read "Read before posting"?

 

[mmm4444bot]

Do you have a textbook? (I don't even know whether or not you're in school.)

Before working with exercises like these, we need to learn about properties of logarithms (which is usually done by studying lessons in school). If you have specific questions about things you don't understand, then you forgot to type them.

Here is one property that you need to memorize, as well as understand how and when to apply it.

log(b^e) = e * log(b)

In other words, when we have the logarithm of a power b^e, we're allowed to remove the exponent e from its base b, and place it in front of the logarithm as a factor.

log(64^7) = 7 * log(64)

Here is another property. Understand it.

log(b * c) = log(b) + log(c)

In other words, when we have the logarithm of a product, we're allowed to rewrite it as the sum of the logarithms of the factors.

log(5 * 20) = log(5) + log(20)

By the time you decide to learn about logarithms, you should already be fluent with squares and cubes of small Natural numbers, as well as the Multiplication Table. Otherwise, you're going to struggle on a wobbly foundation.

2^3 = 8

3^2 = 9

2^3 * 3 = 24

I've given you all the information you need for these exercises. If you don't understand something, then you'll need to ask specific questions. (Which is what you should have done to begin with!)