Chapter 5: Q 105. (page 299)

Solve the equation.
$\log_{2} 8^{x} = - 3$

Short Answer

Expert verified

The solution to the equation, $\log_{2} 8^{x} = - 3$ is, $x = - 1$ .

Step by step solution

Step 1. Given Information

The given equation to be solved is $\log_{2} 8^{x} = - 3$ .

Step 2. Formula used

Rule of change from logarithm to exponents:

$\log_{a} b = y \Rightarrow a^{y} = b$

Step 3. Finding Solution

The given equation is $\log_{2} 8^{x} = - 3$ .

Use rule of change from logarithm to exponents:

$\log_{2} 8^{x} = - 3 2^{- 3} = 8^{x} {(2^{3})}^{x} = (2)^{- 3} (2)^{3 x} = (2)^{- 3} 3 x = - 3 x = - 1$

The solution to the given equationis, $x = - 1$ .

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Solve the equation.
$\log_{2} 8^{x} = - 3$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Formula used

Step 3. Finding Solution

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Solve the equation.
$\log_{2} 8^{x} = - 3$