Sophia College Algebra
MILESTONE 5 RETAKE GUIDE
Southern New Hampshire University
Actual Questions & Verified Answers with Rationales
100% Guarantee Pass
, SCORE
UNIT 5 — MILESTONE 5 19/22
19/22 that's 86% RETAKE
19 questions were answered correctly.
3 questions were answered incorrectly.
1
●
Solve the following logarithmic equation.
x = 250
x = 300
x = 150
x = 200
,RATIONALE
Logarithms and exponents are inverse operations. We can use the base of the logarithm,
10, as a base to an exponent, and place the logarithmic expression as an exponent in the
equation. We'll have to do this to both sides of the equation.
Here, we used 10 as a base number on both sides of the equation. When we do this, the
logarithm and exponent will cancel each other out.
On the left side, the logarithm and exponent cancel each other out, leaving only 5x. On
the right side, is equal to 1000. Finally, divide both sides by 5 to solve for x.
The solution to the equation is x = 200.
CONCEPT
Solving Logarithmic Equations using Exponents
Report an issue with this question
2
●
Write the following as a single rational expression.
,
RATIONALE
Just as with numeric fractions, we can re-write division of algebraic fractions as multiplication
and multiply across numerators and denominators. To re-write fraction division as multiplication,
re-write the second fraction as its reciprocal (flipping the numerator and denominator).
changes to and division changes to multiplication. We can now multiply across the
numerators and denominators.
4 times is equal to and times 1 is equal to . Next, find any common factors in the
numerator and denominator.
Both the numerator and denominator have two factors of x. We can cancel out these factors
and simplify.
Once all common factors have been canceled out in the numerator and denominator, write the
fraction in simplest form.
This is the the simplified fraction written as a single rational expression.
CONCEPT
Multiplying and Dividing Rational Expressions
MILESTONE 5 RETAKE GUIDE
Southern New Hampshire University
Actual Questions & Verified Answers with Rationales
100% Guarantee Pass
, SCORE
UNIT 5 — MILESTONE 5 19/22
19/22 that's 86% RETAKE
19 questions were answered correctly.
3 questions were answered incorrectly.
1
●
Solve the following logarithmic equation.
x = 250
x = 300
x = 150
x = 200
,RATIONALE
Logarithms and exponents are inverse operations. We can use the base of the logarithm,
10, as a base to an exponent, and place the logarithmic expression as an exponent in the
equation. We'll have to do this to both sides of the equation.
Here, we used 10 as a base number on both sides of the equation. When we do this, the
logarithm and exponent will cancel each other out.
On the left side, the logarithm and exponent cancel each other out, leaving only 5x. On
the right side, is equal to 1000. Finally, divide both sides by 5 to solve for x.
The solution to the equation is x = 200.
CONCEPT
Solving Logarithmic Equations using Exponents
Report an issue with this question
2
●
Write the following as a single rational expression.
,
RATIONALE
Just as with numeric fractions, we can re-write division of algebraic fractions as multiplication
and multiply across numerators and denominators. To re-write fraction division as multiplication,
re-write the second fraction as its reciprocal (flipping the numerator and denominator).
changes to and division changes to multiplication. We can now multiply across the
numerators and denominators.
4 times is equal to and times 1 is equal to . Next, find any common factors in the
numerator and denominator.
Both the numerator and denominator have two factors of x. We can cancel out these factors
and simplify.
Once all common factors have been canceled out in the numerator and denominator, write the
fraction in simplest form.
This is the the simplified fraction written as a single rational expression.
CONCEPT
Multiplying and Dividing Rational Expressions
