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anonymous
 one year ago
I've been having a touch of trouble with solving logarithms with uneven bases. For example 8^x10=3^x+2
Now I know that in order to solve I need to
log8^x10=log3^x+2
then you move the power out in front of the logs like so
x10 log8=x+2 log3
this is where I stumble, you find the approximate value of the log soo
(x10)(.903)=(x2)(4.77)
It's after this step were I get lost.
anonymous
 one year ago
I've been having a touch of trouble with solving logarithms with uneven bases. For example 8^x10=3^x+2 Now I know that in order to solve I need to log8^x10=log3^x+2 then you move the power out in front of the logs like so x10 log8=x+2 log3 this is where I stumble, you find the approximate value of the log soo (x10)(.903)=(x2)(4.77) It's after this step were I get lost.

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phi
 one year ago
Best ResponseYou've already chosen the best response.0if it was (x10)*2 = (x2)*3 what would you do? I would distribute, and combine "like terms"

phi
 one year ago
Best ResponseYou've already chosen the best response.0btw, I assume you meant log(3) = 0.47712 (not 4.77)

phi
 one year ago
Best ResponseYou've already chosen the best response.0so do this \[ (x10)(.903)=(x2)(0.477) \\ 0.903x 9.03 = 0.477x 0.954 \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0.426x=.051 /051/.426=.119

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Except x is supposed to = 23.44 ... So I did something wrong

phi
 one year ago
Best ResponseYou've already chosen the best response.0ok, then step by step \[ 8^{(x10)}=3^{(x+2)} \\ \log\left( 8^{(x10)}\right) = \log\left( 3^{(x+2)} \right) \] \[ (x10) \log(8) = (x+2) \log(3) \] rather than approximate the logs, treat them as numbers (which is what they are) \[ x \log(8)  10\log(8) = x \log(3) + 2 \log(3) \\ x \log(8)  x \log(3) = 10\log(8) + 2 \log(3) \\ x ( \log(8)  \log(3) ) = 10\log(8) + 2 \log(3) \\ \] and finally \[ x = \frac{10\log(8) + 2 \log(3) }{ \log(8)  \log(3)} \]

phi
 one year ago
Best ResponseYou've already chosen the best response.0btw, my first equation I managed to write (x2) instead of x+2. That was bad. but, do you follow the steps up above? to get the final answer you need a calculator

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I get 10.57.... not 23.44

phi
 one year ago
Best ResponseYou've already chosen the best response.0what do you get for the top? (btw, I'm getting 23.44102, so it does work out)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I type in 10log(8)+2log(3) and get 9.985...

phi
 one year ago
Best ResponseYou've already chosen the best response.0I get 0.425969 which rounds to 0.4260 to 4 digits but ok now 9.985/ 0.426

phi
 one year ago
Best ResponseYou've already chosen the best response.0if you keep more digits , you will get a more accurate answer

phi
 one year ago
Best ResponseYou've already chosen the best response.0if you type the expression into google like this (10 log 8 + 2 log 3)/(log 8  log 3)= you get out 23.441021894

phi
 one year ago
Best ResponseYou've already chosen the best response.0but I would learn how to use a calculator (it is a useful to know how to do complicated expressions)
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