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Pearson Algebra 2 Common Core, 2011

PA

Pearson Algebra 2 Common Core, 2011 View details

End-of-Course Assessment

Finish the assignment

Exercise 39 Page 967

Use the Properties of Logarithms to eliminate the exponent from the equation.

I

Practice makes perfect

When bases are not the same, we can solve an exponential equation by taking the logarithm of each side of the equation. m=n ⇔ log m = log nNote that in order to take their logarithms, both m and n must be positive numbers. We will start by rewriting the given equation to get a simpler expression.

8.2(3^(2x-4))-11=557.1

LHS+11=RHS+11

8.2(3^(2x-4))= 568.1

.LHS /8.2.=.RHS /8.2.

3^(2x-4) = 568.1/8.2

Let's now solve this equation using the Properties of Logarithms.

3^(2x-4) = 568.1/8.2

log(LHS)=log(RHS)

log (3^(2x-4)) = log (568.1/8.2 )

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Solve for x

log(a^m)= m*log(a)

(2x-4)log 3 = log (568.1/8.2 )

.LHS /log 3.=.RHS /log 3.

2x-4 = log ( 568.18.2 )/log 3

LHS+4=RHS+4

2x = log ( 568.18.2 )/log 3 +4

.LHS /2.=.RHS /2.

x = log ( 568.18.2 )log 3 + 4/2

Write as a sum of fractions

x= log ( 568.18.2 )log 3/2 + 4/2

.a/b /c.= a/b* c

x= log ( 568.18.2 )/2log 3 + 4/2

Use a calculator

x = 3.928871 ...

Round to 1 decimal place(s)

x ≈ 3.9

This corresponds to option I.

Subchapter links

Exercises p.964-971