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October 21, 2025, 09:52:50 pm
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Author Topic: Stark's Method Qs  (Read 4156 times)  Share 

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MrsStark

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Re: Stark's Method Qs
« Reply #15 on: March 31, 2015, 11:09:18 am »
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hey can someone please help me solve for x?

2^(x) X 3^(x+1)= 10
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wobblywobbly

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Re: Stark's Method Qs
« Reply #16 on: March 31, 2015, 06:38:29 pm »
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Quote from: MrsStark on March 31, 2015, 11:09:18 am
hey can someone please help me solve for x?

2^(x) X 3^(x+1)= 10

2^x X 3^x X 3 = 10 (splitting up 3^x+1)

2^x X 3^x = 10/3

(2 X 3)^x = 10/3 (Power rule: (ab)^n = a^n x b^n)

therefore, log6(10/3) = x
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Callum@1373

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Re: Stark's Method Qs
« Reply #17 on: March 31, 2015, 09:13:40 pm »
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Quote from: wobblywobbly on March 31, 2015, 06:38:29 pm
2^x X 3^x X 3 = 10 (splitting up 3^x+1)

2^x X 3^x = 10/3

(2 X 3)^x = 10/3 (Power rule: (ab)^n = a^n x b^n)

therefore, log6(10/3) = x
(2 X 3)^x = 10/3
6^x = 10/3

log6^x = log(10/3)
x X log6 = log(10/3)

x = (log(10/3))/(log6)
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keltingmeith

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Re: Stark's Method Qs
« Reply #18 on: March 31, 2015, 10:09:51 pm »
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Quote from: Callum@1373 on March 31, 2015, 09:13:40 pm
(2 X 3)^x = 10/3
6^x = 10/3

log6^x = log(10/3)
x X log6 = log(10/3)

x = (log(10/3))/(log6)

They are the exact same answer - watch what happens when I change from base 6 to base 10 (with wobblywobbly's answer being base 6, yours being base 10):

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