MHF4U0 | Logarithmic Functions
Questions with complete solution
2025/2026
Exponent Laws - correct answer x^A x x^B = x^(A + B)
x^A / x^B = x^(A-B)
(x^A)^B = x^(A x B)
x^(A/B) = B√(x^A)
What is a log function? - correct answer The inverse of an exponential
function, defined by "base to the power equals what number?"
f(x) = 2^x -> log_2(f(x)) = x
What are the restrictions on log? - correct answer log_a(y) = x
a > 0, a ≠ 1
y>0
If there is more than one term with a variable, take the restriction of all terms
and choose the smallest interval.
How do we apply transformations to log? - correct answer As usual, per
mapping notation or gradually shifting the graph.
, How do we determine the equation of log, given a transformed exponential
function? - correct answer Switch the x and y within the equation and solve
for y once again (remember, log = inverse of exponential).
How do we graph log, given a graph of an exponential function? - correct
answer You can either (A) reflect the function over the y = x line or (B) identify
key points and switch the x and y coordinates.
What happens to the value of the base if it greater than 1? Between 0 and 1?
- correct answer Greater than 1 -> always increases
Between 0 and 1 -> always decreases
How do we evaluate logarithmic expressions? - correct answer For simple
expressions, convert the log function to exponential form and solve (use
exponential laws).
For more complex expressions, use logarithmic laws (comes with practice).
Logarithmic Laws - correct answer ONLY APPLICABLE IF THEY HAVE THE
SAME BASE!!
Product Law: log(xy) = logx + log y
Quotient Law: log(x/y) = logx - logy
Power Law: logx^y = ylogx
What happens when a base is raised to a log base of the same number? (ex.
7^(log_7(49))? - correct answer The number would be the answer. For
example, 7^(log_7(49)) = 7^2 = 49.
Questions with complete solution
2025/2026
Exponent Laws - correct answer x^A x x^B = x^(A + B)
x^A / x^B = x^(A-B)
(x^A)^B = x^(A x B)
x^(A/B) = B√(x^A)
What is a log function? - correct answer The inverse of an exponential
function, defined by "base to the power equals what number?"
f(x) = 2^x -> log_2(f(x)) = x
What are the restrictions on log? - correct answer log_a(y) = x
a > 0, a ≠ 1
y>0
If there is more than one term with a variable, take the restriction of all terms
and choose the smallest interval.
How do we apply transformations to log? - correct answer As usual, per
mapping notation or gradually shifting the graph.
, How do we determine the equation of log, given a transformed exponential
function? - correct answer Switch the x and y within the equation and solve
for y once again (remember, log = inverse of exponential).
How do we graph log, given a graph of an exponential function? - correct
answer You can either (A) reflect the function over the y = x line or (B) identify
key points and switch the x and y coordinates.
What happens to the value of the base if it greater than 1? Between 0 and 1?
- correct answer Greater than 1 -> always increases
Between 0 and 1 -> always decreases
How do we evaluate logarithmic expressions? - correct answer For simple
expressions, convert the log function to exponential form and solve (use
exponential laws).
For more complex expressions, use logarithmic laws (comes with practice).
Logarithmic Laws - correct answer ONLY APPLICABLE IF THEY HAVE THE
SAME BASE!!
Product Law: log(xy) = logx + log y
Quotient Law: log(x/y) = logx - logy
Power Law: logx^y = ylogx
What happens when a base is raised to a log base of the same number? (ex.
7^(log_7(49))? - correct answer The number would be the answer. For
example, 7^(log_7(49)) = 7^2 = 49.
