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If 7^x = 16y and 4^x = 49y then find the value of y-x .

Note by Gaurav Sharma 4 years, 2 months ago

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@sharma...ok..no prob

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@ayanlaja..you are in which grade / standard presently ?

@sharma....(lafin) that good.....do u knw any other educative wapsite or website other than brilliant?

I don't know ..

@sharma.....are u on facebook?

Nope..studious guys in India prefer to be away from such vices

@sharma.......logic? hmm....that good

Yea..because you can't find the exact ( perfect ..and not approximate )value of y by log ..but you can find it in one step by logic

7^x=16y...(1) 4^x=49y....(2) 4rm equation (2)....y=4^x/49 substitutin y=4^x/49 in equation(1) 7^x=164^x/49 7^x49=164^x 7^x7^2=16*4^x 7^(x 2)=2^(2x 4)...(4rm law of indicies) take log of both sides (x 2)log7=(2x 4)log2 (x 2)0.845=(2x 4)0.3010 0.845x 1.69=0.602x 1.204 0.845x-0.602x=1.204-1.69 0.243x=-0.486 x=-0.486/0.243 x=-2 usin equation(2) 4^x=49y y=4^x/49 substitutin x=-2 y=4^-2/49 y=1/16/49 y=0.00138 since x=-2 and y=0.00138 y-x=0.00138-(-2) y-x=0.00138 2 y-x=2.00138

Awesome ! But try solving it by logic ( it's much easier )

2.001

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## Comments

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TopNewest@sharma...ok..no prob

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@ayanlaja..you are in which grade / standard presently ?

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@sharma....(lafin) that good.....do u knw any other educative wapsite or website other than brilliant?

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I don't know ..

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@sharma.....are u on facebook?

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Nope..studious guys in India prefer to be away from such vices

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@sharma.......logic? hmm....that good

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Yea..because you can't find the exact ( perfect ..and not approximate )value of y by log ..but you can find it in one step by logic

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7^x=16y...(1) 4^x=49y....(2) 4rm equation (2)....y=4^x/49 substitutin y=4^x/49 in equation(1) 7^x=16

4^x/49 7^x49=164^x 7^x7^2=16*4^x 7^(x 2)=2^(2x 4)...(4rm law of indicies) take log of both sides (x 2)log7=(2x 4)log2 (x 2)0.845=(2x 4)0.3010 0.845x 1.69=0.602x 1.204 0.845x-0.602x=1.204-1.69 0.243x=-0.486 x=-0.486/0.243 x=-2 usin equation(2) 4^x=49y y=4^x/49 substitutin x=-2 y=4^-2/49 y=1/16/49 y=0.00138 since x=-2 and y=0.00138 y-x=0.00138-(-2) y-x=0.00138 2 y-x=2.00138Log in to reply

Awesome ! But try solving it by logic ( it's much easier )

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2.001

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