how would I solve log(4x+14)^841=2

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how would I solve log(4x+14)^841=2

Mathematics
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so first we need to know what is the base of log(4x+14)
841 log ( 4x + 14 ) = 2 log ( 4x + 14) = 2/841 4x + 14 = e^(2/841) 4x = e^(2/841) - 14 x = [ e^(2/841) - 14]/4
4x+14 is the base

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scrap my answer then
but than the base how can being on exponent ?
841 log ( 4x + 14 ) = 2 log ( 4x + 14) = 2/841 4x + 14 = 10^(2/841) (correction) 4x = 10^(2/841) - 14 (correction) x = [ 10^(2/841) - 14]/4 (correction)
Busterkitten i think you need rewrite please your exersice correct
To cancel log we need to raise to the power of 10 and not e, if it was ln then we would have used e.
log(4x+14) 841=2
- so than you know the logarithm property how we can changeing the base of one logarithm ?
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what is this ?
That's what we have used to cancel the log on one side.
- no - so for example 2 we can rewrite like 2log (base 2) 2 because log(base2)2 =1
Watch this you will understand this logarithmic property. http://patrickjmt.com/properties-of-logarithms-part-2/
Busterkitten - so for this we need to know sure the base of first logarithm for we can rewrite the 2 in the form of this logarithm
hope so much that is understandably sure
If the base is not given it is always 10.
jimmyrep please you make this understandably for ... thank you
nikhil389 - no this not is sure that log sign always log base 10 - so please you check on wikipedia
so for example how i have learned that lg sign the logarithm on base 10
log without base sign logarithm on base 2 and ln sign logarithm on base natural
I think i m really confused what the question actually is, plz rephrase it what is the base ?
- so i think that this can rewrite it sure only Busterkitten
I'm so sorry for the confusion it's log base 4x=14 of 841 = 2
4x+14 i mean
so than you need rewrite the first term of logarithm with base changed
on 841
hope that you will can make it sure
if you know the property of logarithm
so is it 4x+14^2=841
sorry i think this is confused now why you think that like ?
so this is sure that 2 can being rewrit in the form of logarithm like logarithm on base of (4x+14) from (4x+14) squared
so than (4x+14) squared = 841 is it ok ?
can you solve this ?
is it 1.8125?
can you show your calcules please ?
"log" has been highly confused lately; when I was growing up it meant base10, but apparently these days it can be used to express the natural log as well. Without knowing the base (10 or e) we cant really obtain a "correct" answer.
this isn't hard you just have to convert to exponential form to get rid of the log log(b) x = y <--> x = b^y (4x+14)^2 = 841 4x +14 = 29 4x = 15 x = 15/4 = 3.75
hey where did the exponent go?
tanu, i took sqrt of both sides sqrt(x^2) = x

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