Kuoministers
Help me on this question please... I really dont know where to start thanks!!
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Kuoministers
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\[\huge3^{x} + 5 \times 3^{x} = 54\]
DeadShot
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to start, we need to isolate the variables, we start by dividing both sides by 3^x, then subtract 5 from both sides, and then multiply both sides by 3^x
\[3^x + 5 \times 3^x \div 3^x = 54 \div 3^x\]
\[3^x + 5 - 5 = 54/3^x\]
DeadShot
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\[3^x \times 3^x = 54/3^x \times 3^x - 5\]
DeadShot
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\[9^x^2 = 54 -5\]
DeadShot
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\[9^x^2 = 51\]
so now we find the square root of each side
DeadShot
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\[\sqrt{9^x^2} = \sqrt{51}\]
DeadShot
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the square and square root cancel each other out, so it would be \[9^x \approx 7 \]
Kuoministers
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im not sure but thats not the answer that is in the back of the book :P
DeadShot
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divide both sides by 9
\[9^x \div 9 = 7 \div 9\]
\[^x = 7/9\]
Kuoministers
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@artix_17
Kuoministers
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thats not the answer in the book :P
artix_17
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whats your answer?
Kuoministers
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2
Kuoministers
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i think the way he started the question was wrong cause i was told to keep the same base
artix_17
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Yea, 3^x X 3^x can be written as 3^2x
Kuoministers
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yea i agree on that
Kuoministers
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\[\huge3^{2x} + 5 = 3^{3} \times 2\]
this might help?
artix_17
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How did you get that?
rizwan_uet
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|dw:1359366605554:dw|
Kuoministers
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i broke up 54 into 3^3 times 2
cause i wanted to make the base the same which in this case 3
Kuoministers
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I GET IT :D
rizwan_uet
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|dw:1359366719099:dw|
Kuoministers
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i didnt see you could factorise 3^x out of that equation!!
Thanks so much to both of you :)
artix_17
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You can do the 3^x X 3^x = 3^2x
artix_17
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can't*
Kuoministers
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you cant?
artix_17
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No, because its actually 3^x + ( 5 X 3^x )
artix_17
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You have to either solve inside the bracket first or factorize
Kuoministers
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oh thanks @artix_17 for pointing that out!!
I wouldn't have noticed :P
artix_17
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No problem :)