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* = *b ^{x}*, then log

*=*

_{b}y*x*

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

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

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 log_{5}50 – log_{5}2 = log_{8}x for x.

(A) 4

(B) 8

(C) 16

(D) 32

(E) 64

2) If log_{b}(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 log_{b}36 ?

(A) log_{b}9 + log_{b}4

(B) log_{b}72 – log_{b}2

(C) 2log_{b}3 + 2log_{b}2

(D) (log_{b}3)^{2} + (log_{b}2)^{2
}(E) 2log_{b}6

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

(F) -8

(G) -4

(H) 2

(J) 4

(K) 8

5) If log_{b}3 = x and log_{b}2 = y, which of the following is equal to log_{b}72 ?

(A) x^{2}y^{3
}(B) x^{2} + y^{3
}(C) 6xy

(D) 2x + 3y

(E) 3x + 2y

6) If log_{b}2 = 0.8 and log_{b}5 = 1.2 then log_{b } = ?

(F) 0.48

(G) 0.96

(H) 1

(J) 1.2

(K) 2

7) If log_{n } = 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)

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