Chapter 5: Q 92. (page 299)

Solve the equation.
$\log_{x} (\frac{1}{8}) = 3$

Short Answer

Expert verified

The solution to the equation, $\log_{x} (\frac{1}{8}) = 3$ is, $x = \frac{1}{2}$ .

Step by step solution

Step 1. Given Information

The given equation to be solved is $\log_{x} (\frac{1}{8}) = 3$ .

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 $\log_{x} (\frac{1}{8}) = 3$ .

Use rule of change from logarithm to exponents:

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

The solution to the given equationis, $x = \frac{1}{2}$ .

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Solve the equation.
$\log_{x} (\frac{1}{8}) = 3$

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.logx18=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.
$\log_{x} (\frac{1}{8}) = 3$