Chapter 10: Q. 10.47 (page 1030)

Solve:
$a) \log_{a} (121) = 2 b) \ln (x) = 7$

Short Answer

Expert verified

Part (a) The value of $a$ is $11$ .

Part (b) The value of $x$ is $e^{7}$ .

Step by step solution

Step 1. Given information.

The given expressions are,

$a) \log_{a} (121) = 2 b) \ln (x) = 7$

Step 2. Solving part (a).

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

$\log_{a} (121) = 2 a^{2} = 121 a = 11, - 11$

The base of a logarithmic function cannot be negative hence the value of $a$ is $11$ .

Checking the result.

$\log_{a} (121) = 2 \log_{11} (121) = 2 {(11)}^{2} = 121 121 = 121$

Therefore, this is true.

Step 3. Solving part (b).

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

$\ln (x) = 7 e^{7} = x$

Checking the result.

$\ln (x) = 7 \ln (e^{7}) = 7 e^{7} = e^{7}$

Therefore, this is true.

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Solve:
$a) \log_{a} (121) = 2 b) \ln (x) = 7$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Solving part (a).

Step 3. Solving part (b).

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Solve:a)loga121=2b)lnx=7

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Solving part (a).

Step 3. Solving part (b).

One App. One Place for Learning.

Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

Solve:
$a) \log_{a} (121) = 2 b) \ln (x) = 7$