ACT Math › Logarithms
If , then
?
4
5
10
15
25
Calculate the power of that makes the expression equal to 25. We can set up an alternate or equivalent equation to solve this problem:
Solve this equation by taking the square root of both sides.
, because logarithmic equations cannot have a negative base.
The solution to this expression is:
If , then
?
4
5
10
15
25
Calculate the power of that makes the expression equal to 25. We can set up an alternate or equivalent equation to solve this problem:
Solve this equation by taking the square root of both sides.
, because logarithmic equations cannot have a negative base.
The solution to this expression is:
Simplify:
Here, we need to make use of some logarithm identities:
Therefore, putting all of those things together, we get the final answer of
If log4 x = 2, what is the square root of x?
2
3
4
12
16
Given log4_x_ = 2, we can determine that 4 to the second power is x; therefore the square root of x is 4.
Simplify:
Here, we need to make use of some logarithm identities:
Therefore, putting all of those things together, we get the final answer of
If log4 x = 2, what is the square root of x?
2
3
4
12
16
Given log4_x_ = 2, we can determine that 4 to the second power is x; therefore the square root of x is 4.
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
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
Evaluate
log327
9
27
30
3
10
You can change the form to
3_x_ = 27
x = 3
Evaluate
log327
9
27
30
3
10
You can change the form to
3_x_ = 27
x = 3