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Pearson Algebra 2 Common Core, 2011 View details

End-of-Course Assessment

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Exercise 49 Page 968

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

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

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Solve for x

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

log 4 + log 3^x= log 26

SubEqn

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 )