The function g(x) is defined by g(x)=120−3^x.… | GMAT Sprint

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505-555

Algebra

The function g(x) is defined by $g(x)=120−3^x$ . If g(x)=12, then which of the following is true about the value of x?

Answer Choices

Correct answer marked below

0≤x≤3

3<x≤6

Correct

6<x≤12

12<x≤24

24<x≤48

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Explanation

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Official Explanation

Official

To solve for x in the equation

g(x) = 12

, we start with the equation:

120 - 3^x = 12

. Rearranging gives us:

3^x = 120 - 12 = 108

. Next, we can express 108 as a power of 3:

108 = 3^3 * 4 = 27 * 4

. Therefore, we have

3^x = 3^3 * 4

.

Taking logarithms or recognizing that

3^x = 3^3

implies

x = 3

plus some additional factor from the 4.…

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Comments

manishaFeb 9, 2025

Can you explain more?

TiborFeb 23, 2025

Amazing

InaFeb 16, 2025

Thank for sharing!!!

YashApr 22, 2025

Can someone explain it other way?

SankariApr 2, 2024

Thankss

ThomasJun 4, 2024

Great question!

What this question tests

What it tests

Your ability to manipulate linear and quadratic expressions, substitute unknowns, and solve equations under time pressure.

Common trap

Losing a sign when moving terms across the equals sign, or dividing both sides by a variable that could equal zero.

The function g(x) is defined by g(x)=120−3xg(x)=120−3^xg(x)=120−3x. If g(x)=12, then which of the following is true about the value of x?