All Algebra II Resources
Example Questions
Example Question #14 :Logarithms And Exponents
Simplify, if possible:
Notice that the term in the log can be rewritten as a base raised to a certain power.
Rewrite the number in terms of base five.
According to log rules, the exponent can be dropped as a coefficient in front of the log.
The answer is:
Example Question #15 :Logarithms And Exponents
Solve:
Evaluate the log using the following property:
The log based and the base of the term will simplify.
The expression becomes:
The answer is:
Example Question #61 :Logarithms
Try to answer without a calculator.
True or false:
True
False
False
由definition,if and only if. However,
,
making this false.
Example Question #17 :Logarithms And Exponents
Try without a calculator:
Evaluate
None of the other choices gives the correct response.
由definition,if and only if.
8 and 16 are both powers of 2; specifically,. The latter equation can be rewritten as
By the Power of a Power Property, the equation becomes
or
It follows that
,
and
,
the correct response.
Example Question #18 :Logarithms And Exponents
Solve for(nearest tenth):
.
由definition,if and only if. Set, and
if and only if
Through calculation, we see that
.
Example Question #62 :Logarithms
Try to answer without a calculator:
Which is true about?
is an undefined quantity
Cannot be determined
is an undefined quantity
The question asks for the value of the "base 0 logarithm" of 0. However, this is not defined, as a logarithm can only have as its base a positive number not equal to 1.
Example Question #20 :Logarithms And Exponents
Given the following:
Decide if the following expression is true or false:
for all positive.
False
True
True
由definition of a logarithm,
if and only if
Take theth root of both sides, or, equivalently, raise both sides to the power of, and apply the Power of a Power Property:
or
由definition, it follows that, so the statement is true.
Example Question #21 :Logarithms And Exponents
, withpositive and not equal to 1.
Which of the following is true offor all such?
由definition,
If and only if
Square both sides, and apply the Power of a Power Property to the left expression:
It follows that for all positivenot equal to 1,
for all.
Example Question #1 :Logarithms
What is the value ofthat satisfies the equation?
相当于. In this case, you know the value of(对数方程的参数)和b (the answer to the logarithmic equation). You must find a solution for the base.
Example Question #1 :Simplifying Logarithms
Rewrite the following logarithmic expression in expanded form (i.e. as a sum and/or difference):
By logarithmic properties:
;
Combining these three terms gives the correct answer: