# ACT Math: More Logarithm Problems

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
logbMN = logbM + logbN

Quotient Property
logb M/N = logbM – logbN

Power Property
logbMx = xlogbM



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 log4x = 2 for x.

(A)  2
(B)  4
(C)  8
(D)  16
(E)   64

2)  If logb2 = x and logb5 = y, which of the following is equal to logb50 ?

(F)  xy2
(G)  x + y2
(H)  2xy

(J)   x + 2y
(K)  2x + y

3)  In the equation log5x = 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 logb3 = 0.6 and logb5 = 0.9 then logb $\sqrt{15}$ = ?

(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?

logb16 = 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 logx (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)