Recently we posted a review of logarithm rules that included some problems that you might see in the Math section of the ACT. If you’re looking for some more of these problems, we’ve come up with six more you can try. Before you begin, you may wish to again review the rules of logarithms summarized in the table below.

Property
Rule
Product Property
log_{b}MN = log_{b}M + log_{b}N
Quotient Property
log_{b} M/N = log_{b}M – log_{b}N
Power Property
log_{b}M^{x} = *x*log_{b}M

All set on those properties? Great! Now give these problems a try. The answers appear at the bottom of this post.

1) Solve the equation log_{4}x = 2 for x.

(A) 2

(B) 4

(C) 8

(D) 16

(E) 64

2) If log_{b}2 = x and log_{b}5 = y, which of the following is equal to log_{b}50 ?

(F) xy^{2
}(G) x + y^{2
}(H) 2xy

(J) x + 2y

(K) 2x + y

3) In the equation log_{5}x = a, if a is an integer, which of the following CANNOT be a value for x?

(A) 1/25

(B) 1/5

(C) 5

(D) 10

(E) 25

4) If log_{b}3 = 0.6 and log_{b}5 = 0.9 then log_{b } = ?

(F) 0.25

(G) 0.5

(H) 0.75

(J) 1

(K) 1.5

5) In the equation below, if b and x are both integers, which of the following could be the value of b?

log_{b}16 = x

I. b = 2

II. b = 4

III. b = 8

(A) I only

(B) II only

(C) III only

(D) I and II

(E) I, II and III

6) Solve the equation log_{x} (1/27) = -3/2 for x.

(F) -9

(G) -3

(H) 3

(J) 9

(K) 27

If you have questions about these problems or anything else to do with the ACT, leave a comment below or send me an email at info@cardinalec.com .

Solutions:

1) (D)

2) (J)

3) (D)

4) (G)

5) (D)

6) (J)