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Chapter 5: Q. 62 (page 284)

Solve the equation $5^{x} = 5^{- 6}$
and verify your results using a graphing utility

Short Answer

Expert verified

Required solution is {-6}

Step by step solution

01

Step 1. Given information

$5^{x} = 5^{- 6}$

02

Step 2. Calculations

$5^{x} = 5^{- 6} x = - 6 i f a^{u} = a^{v} t h e n u = v$

So the solution set is {-6}

03

Step 3. Graphing solution

Graph $y = 5^{x}$ and $Y = 5^{- 6}$ intersect at (-6, 0.000064)

Hence the required solution set is {-6}.

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Most popular questions from this chapter

Begin with the graph of $y = e^{x}$ and use transformation to graph the function. Determine the domain, range and horizontal asymptote of the function.

$f (x) = - e^{x}$

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$9^{2 x} 27^{x^{2}} = 3^{- 1}$

solve each equation. Verify your results using a graphing utility.

$5^{x^{2} + 8} = 125^{2 x}$

The domain of a one-to-one functiong is $(- \infty, 0)$ , and its range is $[0, \infty)$ . State the domain and the range of $g^{- 1}$ .

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See all solutions

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