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If (400)(6,000) = (240)(100^x), what is the value of x ? : Multiple-choice Questions — Select One Answer Choice

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Re: If (400)(6,000) = (240)(100^x), what is the value of x ? [#permalink]
Hello Brent, if we divide both sides of the equation by \(40\) to get: aren't supposed to (10)(150) = (6)(2.5^x)?

And if we divide both sides of the equation by \(6\) aren't supposed to get (10)/6 (25) = 2.5^x/6? I don't understand how you solved this

Also if I solved it this way 400 = 2^2 x 10^2, 6000 = 2*3*10^3, 240 = 2^3 * 3 * 10, 100 = 10^2 which gives us (2^2 x 10^2) (2*3*10^3) = (2^3*3*10) (10^2x).
Simplify the left and right side to get 2^3*3 x 10^5 = 2^3*3 x 10^1+2x. Can we say it is = 3+1+5 = 3 + 1 + 1 + 2x = 9 = 5 + 2x. Thus x = 2. Does this work?
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If (400)(6,000) = (240)(100^x), what is the value of x ? [#permalink]
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Our goals is to equalize the bases on both sides so that we can compare the exponents. We do this whenever the variable is in the exponent.

Rewriting \((400)(6000)= (240)(100^x)\) as

\((6 \times 4)(100,000) = (240)(100^x) => (24)(100,000) = (240)(100^x)\) gives us

\((100,000)=(10)(100^x)\)

\(10,000 = 100^x\)

\(100^2 = 100^x\)

\(x=2\)

The answer is D.
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Re: If (400)(6,000) = (240)(100^x), what is the value of x ? [#permalink]
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Thank you sir for the reply and amazing clarification
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Re: If (400)(6,000) = (240)(100^x), what is the value of x ? [#permalink]
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Thanks Harish
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Re: If (400)(6,000) = (240)(100^x), what is the value of x ? [#permalink]
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