Mathematics
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OpenStudy (anonymous):
Log
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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
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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):
\[\huge 5^{logx} -3^{logx-1} = 3^{logx+1} - 5^{logx-1}\]
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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
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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
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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