We cover every section of the GMAT with in-depth lessons, 5000+ practice questions and realistic practice tests.

## Up to 90+ points GMAT score improvement guarantee

### The best guarantee you’ll find

Our Premium and Ultimate plans guarantee up to 90+ points score increase or your money back.

## Master each section of the test

### Comprehensive GMAT prep

We cover every section of the GMAT with in-depth lessons, 5000+ practice questions and realistic practice tests.

## Schedule-free studying

### Learn on the go

Study whenever and wherever you want with our iOS and Android mobile apps.

# Powers: Exponential Equations

If $$\displaystyle 3^{-5x} < \frac{1}{243^2}$$, what is the smallest possible integer value of $$x$$?

Correct.

[[Snippet]]

First, convert the negative power of $$3$$ into a positive one (i.e., $$3^{-5x} = \frac{1}{3^{5x}}$$). >$$\displaystyle \frac{1}{3^{5x}} < \frac{1}{243^2}$$ Cross multiply to get $$243^2 < 3^{5x}$$. Express everything as a power of $$3$$. >$$243 = 9 \cdot 27 = 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 = 3^5$$ So $$243^2 < 3^{5x}$$ can be expressed as >$$(3^{5})^{2} < 3^{5x}$$ >$$3^{10} < 3^{5x}$$. Since the bases are the same, the powers can be compared directly. >$$10 < 5x$$ >$$2 < x$$ Hence, the smallest possible integer value of $$x$$ is $$3$$.

Incorrect.

[[Snippet]]

It's true that $$x=6$$ will indeed make the left side smaller than the right side, but did you choose this answer because you missed out on the fact that the question asks for the smallest possible value of $$x$$?

Incorrect.

[[Snippet]]

Incorrect.

[[Snippet]]

Incorrect.

Note that the question uses an inequality, not an equation. If you've done your calculation right, $$x$$ cannot equal $$2$$.

[[Snippet]]

Read the question carefully, and form a strategy before you dive in. The question calls for the smallest value of $$x$$. It actually pays to start plugging in from the smallest value, and moving up until you find the first answer choice that makes the left side of the inequality smaller than the right side.

$$2$$
$$3$$
$$4$$
$$5$$
$$6$$