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)

WritePow

Write as a power

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

PowPow

(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. \

begin{gathered} 6^{3x}= 6^{x+10} \quad \Leftrightarrow \quad 3x = x+10 \end{gathered} Finally, we will solve the equation 3x = x+10.

3x = x+10

SubEqn

LHS-x=RHS-x

2x = 10

DivEqn

.LHS /2.=.RHS /2.

x=10/2

CalcQuot

Calculate quotient

x = 5

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

216^x = 6^(x+10)

Substitute

x= 5

216^5 ? = 6^(5+10)

▼

Simplify

AddTerms

Add terms

216^5 ? = 6^(15)

WritePow

Write as a power

( 6^3 )^5 ? = 6^(15)

PowPow

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

6^(3*5) ? = 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

Exercise 10 Page 303

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