Chapter 10: Q. 10.40 (page 1023)

Find the value of $x$ .
$a) \log_{x} (81) = 2 b) \log_{3} (x) = 5 c) \log_{\frac{1}{3}} (\frac{1}{27}) = x$

Short Answer

Expert verified

Part (a) The value of $x$ is $9$ .

Part (b) The value of $x$ is $243$ .

Part (c) The value of $x$ is $3$ .

Step by step solution

Step 1. Given information.

The given expressions are,

$a) \log_{x} (81) = 2 b) \log_{3} (x) = 5 c) \log_{\frac{1}{3}} (\frac{1}{27}) = x$

Solving part (a).

Here, we will convert the given expression to the exponential form and solve the quadratic equation.

$\log_{x} (81) = 2 x^{2} = 81 x = 9, - 9$

The base of a logarithmic function cannot be negative hence the value of $x$ is $9$ .

Step 3. Solving part (b).

Now, we will convert the given expression to exponential form and simplify.

$\log_{3} (x) = 5 x = 3^{5} x = 243$

Therefore the value of $x$ is $243$ .

Step 4. Solving part (c).

Now, we will convert the given expression to exponential form and simplify.

$\log_{\frac{1}{3}} (\frac{1}{27}) = x {(\frac{1}{3})}^{x} = \frac{1}{27} {(\frac{1}{3})}^{x} = {(\frac{1}{3})}^{3} x = 3$

Therefore the value of $x$ is $3$ .

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Find the value of $x$ .
$a) \log_{x} (81) = 2 b) \log_{3} (x) = 5 c) \log_{\frac{1}{3}} (\frac{1}{27}) = x$

Short Answer

Step by step solution

Step 1. Given information.

Solving part (a).

Step 3. Solving part (b).

Step 4. Solving part (c).

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Short Answer

Step by step solution

Step 1. Given information.

Solving part (a).

Step 3. Solving part (b).

Step 4. Solving part (c).

One App. One Place for Learning.

Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

Find the value of $x$ .
$a) \log_{x} (81) = 2 b) \log_{3} (x) = 5 c) \log_{\frac{1}{3}} (\frac{1}{27}) = x$