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McGraw Hill Glencoe Geometry, 2012 View details

7. Scale Drawings and Models

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Exercise 26 Page 523

Rewrite the terms so that they have a common base.

Practice makes perfect

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

3^x=27^((x-4))

WritePow

Write as a power

3^x=( 3^3 )^((x-4))

PowPow

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

3^x=3^(3(x-4))

Now we have two equivalent expressions with the same base. If both sides of the equation are equal, the exponents must also be equal. 3^x=3^(3(x-4)) ⇔ x=3(x-4) Finally, we will solve the equation x=3(x-4).

x=3(x-4)

Distr

Distribute 3

x=3x-12

SubEqn

LHS-3x=RHS-3x

- 2x=- 12

DivEqn

.LHS /- 2.=.RHS /- 2.

x=6