All ACT Math Resources
Example Questions
Example Question #1 :Logarithms
Let log 5 = 0.69897 and log 2 = 0.30103. Solve log 50
1.68794
1.39794
1.69897
1.30103
1.36903
1.69897
Using properties of logs:
log (xy) = logx+ logy
log (xn) =nlogx
log 10 = 1
So log 50 = log (10 * 5) = log 10 + log 5 = 1 + 0.69897 = 1.69897
Example Question #1 :Logarithms
y = 2x
If y = 3, approximately what is x?
Round to 4 decimal places.
1.5850
2.0000
1.3454
1.8580
0.6309
1.5850
To solve, we use logarithms. We log both sides and get: log3 = log2x
which can be rewritten as log3 = xlog2
Then we solve for x: x = log 3/log 2 = 1.5850 . . .
Example Question #1 :Logarithms
Evaluate
log327
30
3
9
10
27
3
You can change the form to
3x= 27
x= 3
Example Question #1 :How To Find A Logarithm
If, what is?
If, then
Example Question #1 :Logarithms
If log4x = 2, what is the square root of x?
12
4
3
2
16
4
Given log4x= 2, we can determine that 4 to the second power isx; therefore the square root of x is 4.
Example Question #1 :Logarithms
Solve for x in the following equation:
log224 - log23 = logx27
9
3
1
2
–2
3
Since the two logarithmic expressions on the left side of the equation have the same base, you can use the quotient rule to re-express them as the following:
log224–log23 = log2(24/3) = log28 = 3
Therefore we have the following equivalent expressions, from which it can be deduced thatx= 3.
logx27 = 3
x3= 27
Example Question #1 :Logarithms
What value ofsatisfies the equation?
The answer is.
can by rewritten as.
In this form the question becomes a simple exponent problem. The answer isbecause.
Example Question #1 :Logarithms
If, what is?
Use the following equation to easily manipulate all similar logs:
changes to.
Therefore,changes to.
2 raised to the power of 6 yields 64, somust equal 6. If finding the 6 was difficult from the formula, simply keep multiplying 2 by itself until you reach 64.
Example Question #1 :How To Find A Logarithm
Which of the following is a value ofthat satisfies?
The general equation of a logarithm is, and
In this case,, and thus(or, butis not an answer choice)
Example Question #1 :How To Find A Logarithm
How can we simplify this expression below into a single logarithm?
Cannot be simplified into a single logarithm
Using the property that, we can simplify the expression to.
Given thatand
We can further simplify this equation to