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Core Connections Algebra 2, 2013 View details

2. Section 8.2

Finish the assignment

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Exercise 78 Page 393

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. In our case, we need to first isolate the exponential expression. Then we will solve our equation using the Properties of Logarithms.

5.2(3.75)^x = 100

DivEqn

.LHS /5.2.=.RHS /5.2.

(3.75)^x = 100/5.2

log(LHS)=log(RHS)

log (3.75)^x = log 100/5.2

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

x log 3.75 = log 100/5.2

DivEqn

.LHS /log 3.75.=.RHS /log 3.75.

x=log 1005.2/log 3.75

UseCalc

Use a calculator

x≈ 2.2368

Round to 2 decimals

x≈ 2.24

We want to solve the given polynomial equation. To do so, we will apply a factoring technique called the difference of two squares.

a^2-b^2 ⇔ (a+b)(a-b) To do so, we will start by simplifying the equation to obtain the difference of two terms. Then, we will write both terms as perfect squares.

4+3x^4=81

SubEqn

LHS-4=RHS-4

3x^4 = 77

DivEqn

.LHS /3.=.RHS /3.

x^4 = 77/3

SubEqn

LHS-77/3=RHS-77/3

x^4 - 77/3 = 0

SplitIntoFactors

Split into factors