# ACT Math: Logarithms

The math on the ACT goes deeper into the high school math curriculum than does the math on the SAT.  One of these more advanced topics is logarithms.  Logarithmic and exponential functions are related to each other.  You should know the properties of both and be able to convert from one type of function to the other.  The relationship between the two functions is the following:

If y = bx, then logby = x

It is also important that you know the properties of logarithms.



Property
Rule

Product Property
logbMN = logbM + logbN

Quotient Property
logb M/N = logbM – logbN

Power Property
logbMx = xlogbM



Here are some problems involving logarithms that are similar to those you could see on the ACT Math test.  Give them a try.  The solutions appear at the bottom of this post.

1)  Solve the equation log550 – log52 = log8x for x.

(A)  4
(B)  8
(C)  16
(D)  32
(E)   64

2)  If logb(23/4)3 = 3, then b is ?

(F)   between 1 and 2
(G)  between 2 and 3
(H)  between 3 and 4
(J)    between 4 and 5
(K)   between 5 and 6

3)  Which of the following is NOT equal to logb36 ?

(A)  logb9 + logb4
(B)  logb72 – logb2
(C)  2logb3 + 2logb2
(D)  (logb3)2 + (logb2)2
(E)  2logb6

4)  Solve the equation logx (1/8) = -3/2 for x.

(F)  -8
(G)  -4
(H)  2
(J)   4
(K)  8

5)  If logb3 = x and logb2 = y, which of the following is equal to logb72 ?

(A)  x2y3
(B)  x2 + y3
(C)  6xy

(D)  2x + 3y
(E)  3x + 2y

6)  If logb2 = 0.8 and logb5 = 1.2 then logb $\sqrt{10}$ = ?

(F)  0.48
(G)  0.96
(H)  1
(J)   1.2
(K)  2

7)  If logn $\frac{(n^{10})^{^{2}}}{n^{5}}$ = x, then the value of x is

(A)  4
(B)  7
(C)  8
(D)  12
(E)  15

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)  (E)
2)  (K)
3)  (D)
4)  (J)
5)  (D)
6)  (H)
7)  (E)