Question

solve \[2^{6x-1}=28\] and check

Answer 1

to start, take the natural log of both sides.

Answer 2

so ...
\[\ln 2^{6x-1} = \ln 28\]
?

Answer 3

cool. Now use power rule to bring out the (6x-1)

Answer 4

(6x-1)ln2=ln28

Answer 5

excellent! now divide both sides by ln2

Answer 6

uhh... 6x-1=4.807355

Answer 7

you can leave this part as the exact answer - usually don't need to go to decimal answer

Answer 8

6x-1 = ln(28)/ln(2)

Answer 9

so leave it as ln28/ln2 ?
is that what you mean?

Answer 10

yep. It will depend on what format your answer need to be in. Do the instructions say to answer in terms of natural logs, or as a decimal?

Answer 11

it just says to solve the equation for x and check the solution.
the answer, however, is kept in terms of log.

Answer 12

ok. So you should leave this part as ln28/ln2

Answer 13

ok, i did up to that part, but now idk what to do... i have the answer, idk how to get to it.

Answer 14

To finish solving for x, add one to both sides and divide both sides by 6
6x = ln28/ln2 + 1

x = ln28/(6ln2) + 1/6

Answer 15

there are several ways to write this answer...

Answer 16

my worksheet tells me that x=log56/6log2

Answer 17

Your answer and their answer are the same amount - check using a calc
we started using ln but the solution is the same as using log. So

ln28/(6ln2) + 1/6 is the same as log28/(6log2) + 1/6

Answer 18

wait before we go any further, would it be ln28/(6ln2)
or ln28/ln2 +1/6 ??
sorry i got lost

Answer 19

both terms have to be divided by 6
\[\large 6x = \frac{\ln28}{\ln2} + 1\]
\[\large \frac{1}{6} \cdot 6x = \frac{1}{6} \cdot \frac{\ln28}{\ln2} + \frac{1}{6} \cdot1\]
\[\large x = \frac{\ln28}{6\ln2} + \frac{1}{6}\]

Answer 20

oooh okay,

Answer 21

how come it is log56/6log2 then?
where did the log56 come from? :S

Answer 22

To get this answer to look like their answer we just need to multiply the 1/6 by ln2/ln2
\[\large x = \frac{\ln28}{6\ln2} + \frac{1}{6}\cdot\frac{\ln2}{\ln2}\]
\[\large x = \frac{\ln28}{6\ln2} + \frac{\ln2}{6\ln2}\]
since the fractions have a common denominator, we can add
\[\large x = \frac{\ln28 + ln2}{6\ln2} \]
then use product rule to write the numerator as one ln

Answer 23

oooh ! okay. that makes sense.
sorry another question.
when i plug in ln28/(6ln2)+1/6
and ln28/(6ln2)+1/6
i get .55162
and .23927

... :S am i doing it wrong?

Answer 24

???

Answer 25

oh... LOL oooppsss. i put the eqn in wrong in my calculator then.. ._.

Answer 26

k thanks @cruffo (:

Answer 27

np