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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 49 Page 968

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

H

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 n Note that in order to take their logarithms, both m and n must be positive numbers. Let's now solve our equation using the Properties of Logarithms.

4(3^x)=26

log(LHS)=log(RHS)

log (4(3^x))= log 26

▼

Solve for x

log(mn)=log(m) + log(n)

log 4 + log 3^x= log 26

LHS-log 4=RHS-log 4

log 3^x= log 26 - log 4

log(m) - log(n)=log(m/n)

log 3^x = log (26/4 )

a/b=.a /2./.b /2.

log 3^x = log (13/2 )

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

xlog 3 = log (13/2 )

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

x = log ( 132 )/log 3

Use a calculator

x=1.703787 ...

Round to 1 decimal place(s)

x ≈ 1.7

Therefore, the correct option is H.

Subchapter links

Exercises p.964-971