A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 5 years ago
How can I simplify this:
log10(4)log10(2)
Please help
anonymous
 5 years ago
How can I simplify this: log10(4)log10(2) Please help

This Question is Closed

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0log(ab) = log a + log b so log 10(4) log 10(2) = (log10 + log4)(log 10+log2) log 10 = 1 (log10 + log4)(log 10+log2)=(1+log4)(1+log2)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I dont get it. But the original expression was: \[Log _{16}(a)+Log _{4}(a)+Log _{2}(a)\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I was trying to change the log to a unique base. and I got: \[\log(a)=7Log(16)Log(4)Log(2)/(\log4Log2+Log16*Log2+Log16*Log4)\] I got stacked there

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0are you asked to find log(a)?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i think the expression isn't complete Log16(a)+Log4(a)+Log2(a) it should be an equation or you can't find a

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yeah I was thinking about that too. Ok thanks

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Sorry the expresion was: Log16(a)+Log4(a)+Log2(a) =7

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0do you think the equation can be solved now?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0can you explain it to me. I tried really hard and I got no much further.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0log16a.4a.2a = 7 log(2^7)(a^3) = 7 7 equals to log 10^7 so log (2^7)(a^3) = log 10^7 (2^7)(a^3) = 10^7 a^3 = 10^7 / 2^7 = (10/2)^7 a^3 = 5^7 a = 5^(7/3)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i got 2^7 from 16x4x2 16 is 2^4 and 4 is 2^2 therefore 16x4x2 = 2^7

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0what do you mean by: Log16a.4a.2a = 7 \[Log(16a*4a*2a)\] Is 10 the base? How did you end up with that?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes , if the base isn't written, it means the base is 10. one of the identities of logarithm is loga + logb = log(ab)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Remember the original expression has different bases. \[Log _{16}(a)+Log _{4}(a)+Log _{2}(a)=7\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh sorry, i thought the 16 is inside the logarithm. so the base is 16, 4 and 2? wait a moment i'll try solve it again

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok i got it 16 = 2^4 and 4\[a ^{c}\]= 2^2 so \[\log _{2^4}a + \log _{2^2}a + \log _{2}a = 7\] the identity of logarithm: \[\log _{a^b}c = (1/b)logc\] \[(1/4)\log _{2}a + (1/2)\log _{2}a + \log _{2}a = 7\] \[(7/4)\log _{2}a = 7\] \[\log _{2}a = (4/7) 7 = 4\] we know that if \[\log _{a}b = c \] then \[a ^{c}=b\] \[\log _{2}a = (4/7) 7 = 4\] therefore \[2^{4} = a\] a=16

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0dont mind anything i type above the sentence " the identity of logarithm", it's typo

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yeah i was thinking about that. Let me check it out and try to understand it. Thanks dude

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\log_{a ^{b}}x ^{y}=(y/b)\log_{a}x \] put 16 and 4 as a power of 2..and use the above log property. hope this would help

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yeah thanks. It is clear now
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.