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Example Questions
Example Question #1 : Logarithms
Let log 5 = 0.69897 and log 2 = 0.30103. Solve log 50
1.36903
1.39794
1.30103
1.69897
1.68794
1.69897
Using properties of logs:
log (xy) = log x + log y
log (xn) = n log x
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
0.6309
2.0000
1.8580
1.3454
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 #3 : How To Find A Logarithm
Evaluate
log327
9
3
30
10
27
3
You can change the form to
3x = 27
x = 3
Example Question #1 : Logarithms
If , what is
?
If , then
Example Question #5 : How To Find A Logarithm
If log4 x = 2, what is the square root of x?
2
3
4
12
16
4
Given log4x = 2, we can determine that 4 to the second power is x; therefore the square root of x is 4.
Example Question #1 : How To Find A Logarithm
Solve for x in the following equation:
log224 - log23 = logx27
–2
1
9
3
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 that x = 3.
logx27 = 3
x3 = 27
Example Question #2281 : Act Math
What value of satisfies the equation
?
The answer is .
can by rewritten as
.
In this form the question becomes a simple exponent problem. The answer is because
.
Example Question #8 : How To Find A Logarithm
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, so must equal 6. If finding the 6 was difficult from the formula, simply keep multiplying 2 by itself until you reach 64.
Example Question #1 : Logarithms
Which of the following is a value of that satisfies
?
The general equation of a logarithm is , and
In this case, , and thus
(or
, but
is not an answer choice)
Example Question #1 : Logarithms
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 that and
We can further simplify this equation to
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