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?

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.

Thank you sir for the reply and amazing clarification

Thanks Harish