Ask your own question, for FREE!
Mathematics 20 Online
OpenStudy (anonymous):

Log

OpenStudy (sweetburger):

twig

Parth (parthkohli):

calc

OpenStudy (anonymous):

\[\huge 5^{logx}-3^{\log-1} = 3^{logx+1} - 5^{logx-1}\]

OpenStudy (anonymous):

Bring 3's and 5's together that would the start

OpenStudy (anonymous):

@mathslover

mathslover (mathslover):

log-1 ? is it log (-1) ?

OpenStudy (anonymous):

logx -1

mathslover (mathslover):

Okay..

mathslover (mathslover):

Seems easy now... Let logx = y \(5^{y} -3^{y-1} = 3^{y+1} -5^{y-1} \)

OpenStudy (anonymous):

\[\huge 5^{logx} -3^{logx-1} = 3^{logx+1} - 5^{logx-1}\]

OpenStudy (sweetburger):

wish i thought of that sooner @mathslover

OpenStudy (anonymous):

It ,Didn't strike me before

mathslover (mathslover):

\(\large 5^{y} + 5^{y-1} = 3^{y+1 } + 3^{y-1} \)

mathslover (mathslover):

\(5^{y} \left( 1 + \cfrac{1}{5} \right) = 3^{y} \left( 3 + \cfrac{1}{3} \right) \) \(\left(\cfrac{5}{3} \right)^ y =\cfrac{10}{3} \times \cfrac{5}{6} \)

mathslover (mathslover):

Simplify RHS Equate the powers and find y Equate y = log x Find x

OpenStudy (anonymous):

\[\huge [\frac{ 5 }{ 3 }]^{y} = \frac{ 25 }{ 9 }\]

OpenStudy (anonymous):

@mathslover are u there

mathslover (mathslover):

Sorry, was away!

mathslover (mathslover):

\(\left(\cfrac{5}{3}\right)^y = \left(\cfrac{5}{3}\right)^2 \) Thus, y = 2 \(\log x = 2\)

OpenStudy (anonymous):

so 100

OpenStudy (anonymous):

tysm

mathslover (mathslover):

Yeah, if the base is 10, then it will be \(10^2\) . If the base is "e" then it will be \(e^{2} \)

mathslover (mathslover):

You're welcome. Good Luck! @No.name

Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!
Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!