Log question

Question

Log question

abbles · Answer

attachment

abbles · Answer

I did 5logb(A) + 2logb(C) - 6logb(D)
Then I substituted...
3^5 + 2^2 - 5^6 = -15,378

abbles · Answer

The answer choices are:
-15,378
-11
2
There isn't enough information.

sweetburger · Answer

actually there is an easier way lool

abbles · Answer

Haha. Share

mathstudent55 · Answer

I think this problem is meant for you to use these rules of logs:

$\log ab = \log a + \log b$

$\log \dfrac{a}{b} = \log a - \log b$

$\log a^n = n \log a$

abbles · Answer

5logb(A) + 2logb(C) - 6logb(D) right?

sweetburger · Answer

$$(5\log_b(A)+2\log_b(C))-6\log_b(D)$$

sweetburger · Answer

yea dont forgot the parenthesis

mathstudent55 · Answer

Use those three rules to simplify the log of the fraction into the sum and difference of logs. Also use the log of a power rule to make the exponent into a coefficient.
Then substitute the given logs into your expression.

abbles · Answer

sweetburger, why does it need parenthesis?

mathstudent55 · Answer

You don't need the parentheses around the sum of logs because by the order of operations, you will do the sum before the subtraction anyway.

abbles · Answer

That's what I thought :P

abbles · Answer

Sweetburger, what is the next step? substitute?

mathstudent55 · Answer

$5log_bA + 2log_bC - 6\log_b D$

$log_bA = 3$

$log_bC = 2$

$\log_b D = 5$

Substitute the log values above.

abbles · Answer

3^5 + 2^2 - 5^6 ?

abbles · Answer

@mathstudent55  Would the answer be -15,378 ?

abbles · Answer

Or would it be 5(3) + 2(2) - 6(5) ? which equals -11

abbles · Answer

@sweetburger do you know?

mathstudent55 · Answer

I don;t know where the exponents are coming from.
Your expression has no exponents.
Just substitute the logs and find the result.
The answer is -11.
Your second answer is correct.

mathstudent55 · Answer

I don't know where the exponents are coming from.
Your expression has no exponents.
Just substitute the logs and find the result.
The answer is -11.
Your second answer is correct.

mathstudent55 · Answer

$5log_bA + 2log_bC - 6\log_b D = 5 \times 3 + 2 \times 2 - 6 \times 5
= 15 + 4 - 30 = -11$

abbles · Answer

I was confused because 5logb(A) is the same thing as logb(A)^5 right?

Thanks for coming back!

mathstudent55 · Answer

$5 \log_b A = \log_b A^5$ is correct, but you don't know what $\log_b A^5$ is.

$\log_b A^5$ is not necessarlily equal to $(\log_b A)^5$

You only know what $\log_b A$ is.

That is why you needed to use the rule of the exponents to make the exponent a coefficient, so then you can just replace the log by the value you were told.

abbles · Answer

Ah, okay :) Thanks a bunch

mathstudent55 · Answer

You're welcome.