Question

Solve the inequality graphically. 4^x > 2^x

A. x > 0
B. x < 0
C. x > 1
D. x < 1

Answer 1

A. x > 0

Explanation:

see graph

4^x > 2^x

Replace 4 with 2^2

2^2^x > 2^x

a^b^x = a^(b*c) so

2^ 2x > 2^x

If the bases are the same, the exponents must keep the same ratio

2x>x

This is true if x>0

Answer 2

A. x > 0

Explanation:

As long as the number (x) is a number greater than 0, the inequality would be correct. Take for example, 1 (a number greater than 0)

4^1 = 4; 2^1 = 2; 4 > 2

Another example is 2

4^2 = 16; 2^2 = 4; 16 > 4

etc.

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