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Big Ideas Math Integrated I, 2016

BI

Big Ideas Math Integrated I, 2016 View details

4. Solving Exponential Equations

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Exercise 10 Page 303

Rewrite the terms so that they have a common base.

x=5

Practice makes perfect

To solve the given exponential equation, we will start by rewriting the terms so that they have a common base.

216^x = 6^(x+10)

Write as a power

( 6^3 )^x = 6^(x+10)

(a^m)^n=a^(m* n)

6^(3x)= 6^(x+10)

Now, we have two equivalent expressions with the same base. If both sides of the equation are equal, the exponents must also be equal. 6^(3x)= 6^(x+10) ⇔ 3x = x+10 Finally, we will solve the equation 3x = x+10.

3x = x+10

LHS-x=RHS-x

2x = 10

.LHS /2.=.RHS /2.

x=10/2

Calculate quotient

x = 5

To check our answer, we will substitute 5 for x in the given equation.

216^x = 6^(x+10)

▼

x= 5

216^{{\color{#0000FF}{5}}} \stackrel{?}{=} 6^{{\color{#0000FF}{5}}+10}

Add terms

216^{{\color{#0000FF}{5}}} \stackrel{?}{=} 6^{15}

Write as a power

\left( 6^3 \right)^{5} \stackrel{?}{=} 6^{15}

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6^{3\cdot5} \stackrel{?}{=} 6^{15}

Multiply

6^(15) = 6^(15) ✓

Since substituting 5 for x in the given equation produces a true statement, x=5 is the solution to our equation.

Subchapter links

Communicate Your Answer p.299

Monitoring Progress p.300-302

Exercises p.303-304