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anonymous
 5 years ago
how do u solve log of x 5=1/4
anonymous
 5 years ago
how do u solve log of x 5=1/4

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You need to be a little clearer. Is it,\[\log_x5=\frac{1}{4}\]or\[\log x^5=1/4\]?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0one sec...dealing with a couple of things at once.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You have to use the definition of what the logarithm means. If you have\[y=a^x\]then by definition of the logarithm,\[\log _a y = x\] By the definition then, you have\[\log_x 5 = 1/4 \rightarrow x^{1/4}=5\]Raise both sides to the power of 4, and you have\[(x^{1/4})^4=5^4 \rightarrow x=625\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i have another u could help me with

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok baseballkid, but I could use another fan :p

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ln(5x3)+ln2 ln(242x)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0how do i become your fan

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You have to know your log laws. The two you need here are:\[\log a + \log b = \log ab\]and\[\log a  \log b = \log \frac{a}{b}\]Here, for the frist two terms, you have\[\ln ( 5x3)+\ln 2 = \ln (2(5x3))=\ln (10x6)\]and then\[\ln (10x6) \ln (242x)= \ln \frac{10x6}{242x}=\ln \frac{5x3}{12x}\]since the numerator and denominator have a common factor of 2.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok im an idiot i put it in wrong i meant to put ln(5x3) + ln2 = ln(242x)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0but why r u so smart? i mean i think its great

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Okay. Now you're solving for x...that's different.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0lol, so smart...thanks...

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You need to exponentiate both sides of your equation:\[e^{\ln(5x3)+\ln2}=e^{\ln(242x)} \rightarrow e^{\ln2(5x3)}=e^{\ln(242x)}\]\[\rightarrow 2(5x3)=242x\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You expand and solve for x now.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Do you see what I did with exponentiation? It 'undoes' the logarithm. It's the 'inverse' of logarithm.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Once you are done with this, could you please provide me some help

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I may have to just take a look and go. I'm supposed to be elsewhere today.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Ok it will only take a look from a genius like you Here it is http://openstudy.com/groups/mathematics#/updates/4da834d1d6938b0bf8d5a44d

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0baseballkid, are you okay with this? If not, leave a message here and when I can, I'll get back to you.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok thank you so much. i have some more ill post later

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0post them for others in the question box if you need them quickly (others will do them), else, post here and I'll do what I can. :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\log_{5} (3x+10)3\log_{5}4=2 \]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You have to use the log laws,\[\log_5 (3x+10)3\log _ 5 4 =\log_5 (3x+10)\log _ 5 4 ^3\]\[=\log 5 \frac{3x+10}{64}\]that is,\[\log _ 5 \frac{3x+10}{64}=2 \rightarrow \frac{3x+10}{64}=5^2\]by definition of the logarithm. Solving for x, you have\[3x+10=25 \times 64 \rightarrow x = 530\]
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