All SAT II Math II Resources
Example Questions
Example Question #2 : Exponents And Logarithms
Solve for
:
Give your answer to the nearest hundredth.
The equation has no solution.
Take the common logarithm of both sides and solve for
:
Example Question #1 : Exponents And Logarithms
Solve for
:
Give your answer to the nearest hundredth.
The equation has no solution.
Take the natural logarithm of both sides and solve for
:
Example Question #1 : Exponents And Logarithms
To the nearest hundredth, solve for
:
Take the common logarithm of both sides, then solve the resulting linear equation.
Example Question #1 : Exponents And Logarithms
To the nearest hundredth, solve for
:
The equation has no solution.
Take the common logarithm of both sides, then solve the resulting linear equation.
Example Question #3 : Exponents And Logarithms
Solve for
:
Take the common logarithm of both sides:
Example Question #1 : Exponents And Logarithms
Solve for
:
The base of the common logarithm is 10, so
The sum of three logarithms is the logarithm of the product of the three powers, so:
Therefore,
Example Question #13 : Mathematical Relationships
To the nearest hundredth, solve for
:
Example Question #4 : Exponents And Logarithms
Solve for
:
The equation has no solution
The base of the common logarithm is 10, so
The sum of logarithms is the logarithm of the product of the three powers, and the difference of logarithms is the logarithm of the quotient of their powers. Therefore,
Example Question #11 : Mathematical Relationships
Give the set of real solutions to the equation
(round to the nearest hundredth, if applicable)
The equation has no solution.
Using the Product of Powers Rule, then the Power of a Power Rule, rewrite the first two terms strategically:
Substitute
for ; the equation becomes
Factor this as
by finding two integers whose product is 3 and whose sum is
. Through some trial and error we find , so we can write
By the Zero Product Rule, one of these two factors must be equal to 0.
If
, then .Substituting
back for :
.
If
, then .Substituting
back for :
Both can be confirmed to be solutions by substitution.
Example Question #41 : Sat Subject Test In Math Ii
Give the solution set:
The equation has no solution.
Rewrite by taking advantage of the Product of Powers Property and the Power of a Power Property:
Substitute
for ; the resulting equation is the quadratic equation
which can be written in standard form by subtracting
from both sides:
The trinomial can be factored by the
method, Look for two integers with sum and product ; by trial and error, we find they are , so the equation can be rewritten and solved by grouping:
By the Zero Product Property, one of these factors must be equal to 0.
Either
Substituting
back for :
Or:
Substituting
back for :
The solution set, as can be confirmed by substituting in the equation, is
.All SAT II Math II Resources
