Question

solve 2 log 3 x = 54

Answer 1

is it
\[2\log_3(x)=54\]?

Answer 2

yea........ it is base 3

Answer 3

log 3(x) = 27.......?

Answer 4

thought so
divide both sides by two and start with
\[\log_3(x)=27\] then it should be fairly obvious

Answer 5

x = 9.....? my only doubt?

Answer 6

on no

Answer 7

ohh wait...

Answer 8

it is 3^27........?

Answer 9

\[\log_b(x)=y\iff b^y=x\]they are trying to trick you

Answer 10

yes, the answer is \(x=3^{27}\)

Answer 11

no don't fall for the trick!

Answer 12

but how come the answer is 7.6256.......... whereas 3^27 is a huge #

Answer 13

probably written in scientific notation
let me check

Answer 14

ok

Answer 15

1) Divide both sides by 2
\[\log_{3} x=54/2\]\[\log_{3} x=27\]\[a=\log_{b} (b^a)\]\[\log_{3} x=\log_{3} (3^(27)\]
x=3^27

Answer 16

how'd i guess?
\[3^{27}=7.625597484987 × 10^{12}\]

Answer 17

yea but @Abmon98 ........by that we get 7625597........ and so on..... but the answer here is only 7.6256

Answer 18

scientific notation is being used

Answer 19

@satellite73 ............ hmm i see........ they didnt ask for scientific notation...... and the answer only states 7.6256........... that's it..... not even raised to something..... so i was wondering....??

Answer 20

i don't know what you mean by "the answer states"

Answer 21

ohh @satellite73 ....... i meant that answer only says 7.6256 and nothing like 7.6 x 10^12...............but dont worry....i got it.........bdw thx a lot for all the help..!!

Answer 22

I don't have the solution i've forgotten a lot but I know that when you multiply numbers you add the logs. 54 can be expressed as 2 *27 which is 2* 3^3
so it would be Log base 3 of 2 plus log base 3 of 3^3 3 log to base 3 of 3 = 3