3 Questions: 2 on Range and 1 on a logarithm

**qbkr21** · October 22nd 2006, 04:01 PM

Ok great thanks

**qbkr21** · October 22nd 2006, 04:14 PM

What about the other problem on logs do you guys have any clue on that one?

**topsquark** · October 22nd 2006, 05:07 PM

Originally Posted by qbkr21

3. When Log base b of A=2 and Log base b of D=5

What is: Log base b of (a+d)

$log_bA = 2$

$log_bD = 5$

I presume you want to know: $log_b(A+D)$ ? (Yes, case is important. A is not necessarily the same as a.)

I couldn't tell you. With the given information I could tell you what $log_b(AD)$ is (its 2 + 5 = 7).

Let me show you why this is so hard.

$log_bA = 2$ means that $b^2 = A$ . Similarly $log_bD = 5$ means $b^5 = D$ . So
$A + D = b^2 + b^5$

But this is NOT a simple power of b. There IS an exponent c such that $b^c = b^2 + b^5$ , but this is not an easy equation to solve for a general value of b, if it's even possible to do generally. (However if we know the value of b we can numerically estimate it.)

If it still seems simple, try to find c for $2^c = 2^2 + 2^5 = 4 + 32 = 36$ . So $c = log_236 \approx 5.169925001$ . But if b = 3, then $c = log_2252 \approx 5.033103256$ .

-Dan

**ThePerfectHacker** · October 22nd 2006, 05:10 PM

I think he wants to know,
$\log_b (A\cdot D)$
Not, $\log_b(A+B)$
It seems that either he copied wrong of his teacher posed an unfair problem.

**qbkr21** · October 22nd 2006, 05:20 PM

Dan you are right I did A time D and got 15 and that was wrong on the test. Maybe I am in way over my head, I might should have just added them. But when you expand logs through mulitiplication you add them, this is what I thought but as stated she marked it wrong. My teacher obviously wanted something totally different. Thanks Guys.

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