SAT Math XIX

Algebra Level 1

If $y=3^x$ and $x$ and $y$ are both integers, which of the following is equivalent to $9^x+3^{x+1}$ ?

y(y+3)

y^3

3(y+3)

y^2+3

1 solution

John M.
Oct 3, 2014

$y=3^x$ .

Notice that $9^x$ is same as $(3^2)^x$ , or $(3^x)^2$ , which is $y^2$ .

$(3^x)^2=(y)^2$

Also, notice that $3^{x+1}=3\cdot 3^x$ (since the exponent simply tells how many times the base is multiplied by itself), which is $3y$ .

$3\cdot 3^{x}=3\cdot y$

Combining,

$9^x+3^{x+1}=y^2+3y=\boxed{y(y+3)}$

A part of the SAT Math set.

The uniqueness of your solutions are explanations.I think hardly anyone explains in brilliant like @John Muradeli .

Soumo Mukherjee - 6 years, 7 months ago

Yeah I'm heavily conceptual and try to minimize it on operations. I think the problem most people have with math is the understanding behind the actual skeleton of the mathematical operations - which is not their fault, most schools teach like that.

And since this is the SAT, my solution is directed towards the less mathematically experienced audiences (because math pros don't need SAT prep xD).

But yeah I always try to make it all clear. Thanks for the compliment :)

John M. - 6 years, 7 months ago

SAT Math XIX

1 solution

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