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anonymous
 5 years ago
Log4 Xlog16 (x+3)=1/2
The 4 and 16 are bases can someone please tell me how to solve this?
anonymous
 5 years ago
Log4 Xlog16 (x+3)=1/2 The 4 and 16 are bases can someone please tell me how to solve this?

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amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0change of base perhaps??

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.04^y = x 16^y3 = x would that work out ?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0change both bases to 4, then use the laws of exponents to combine\[\log_{16}(x+3)=y\] means \[16^y=(x+3)\] \[4^{2y}=x+3\] \[2y=log_4(x+3)\] \[y=\frac{log_4(x+3)}{2}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0change of base gets me two joined equations with a factored out x

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0log4(x)  [log4(x+3)/log4(16)] = 1/2 log4(x)  (1/2)log4(x+3) = 1/2

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0idk if i can change both bases to 4

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0log4(x/sqrt(x+3)) = 1/2

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0sqrt(4) = sqrt(x/(x+3)) i believe so :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0then exponentiate to get \[\frac{x}{\sqrt{x+3}}=4^{\frac{1}{2}}\]

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.04 = x/x+3 4x+12 = x 3x = 12 x = 4...maybe

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0i got lost in it for a moment....

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0no way 4 is an answer since you cannot take log of 4

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0i know i know.... my brain took a momentary leave of absence lol

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the 4 is not negative

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0sqrt(4) = x/(x+3) is what i meant to type :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.04x^2 +24x +36 = x^2 3x^2 +24x +36 = 0... thats better me thinks

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0x = 6 and 2 by that accounting...... so maybe not ;)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oops start with \[\frac{x}{\sqrt{x+3}}=4^{\frac{1}{2}}\]

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0...... yeah, it would help if I did the actual problem instead of making up me own lol

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[x^2=4(x+3)=4x+12\] \[x^24x12=0\] \[(x6)(x+2)=0\] \[x=6, x=2\] 2 not a solution. we can try 6 to see if it works.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0hey where did the log16 go?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0we..and be that i me sat.... modified it to a log4(x+3)/2

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I get it its just i do not know where the log16 went the log of16 is 1.20411

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0change of base just changes the appearance and not the value

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0let us go slow. \[log_{16}(x)=y\] means \[16^y=x\] for example \[log_{16}(4096)=3\] because \[16^3=4096\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0but \[16=4^2\] so it is also true that \[(4^2)^3=4069\] \[4^6=4069\] so \[log_4(4069)=6\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so the log base 16 did not disappear, just converted to log base 4

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oho i get it thank you :]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0how did you get that? i am fairly certain x = 6
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