Chapter 2: Q. 2.14 (page 62)

Write $e^{10^{23}}$ in the form $10^{x}$ , for some $x .$

Short Answer

Expert verified

The value in the form as $e^{10^{23}} = 10^{(4.343 \times 10^{22})} .$

Step by step solution

Step: 1 Using logarithmic function:

The natural logarithm, which has $e$ as its base, is the most frequent exponential function in physics and mathematics due to its straightforward features. However, logarithms may be defined in terms of any other real number, and the definition is similar to that of natural numbers. The base ten logarithms are defined as follows:

$10^{\log (x)} = x$

Taking logarithm on both sides and using $\ln (a^{b}) = b \ln (a)$ ,we have

$\begin{array}{l} \ln (10^{\log (x)}) = \ln (x) \\ \log (x) \ln (10) = \ln (x) \end{array}$

Converting base as exponentiation form as

$e^{10^{23}} = 10^{x}$

Step: 2 Finding value in form:

Taking logarithm on above equation,

$\begin{array}{l} e^{10^{23}} = 10^{x} \\ \ln (e^{10^{23}}) = \ln (10^{x}) \end{array}$

If $\ln (e^{a}) = a; \ln (b^{a}) = a \ln (b)$ so,

$\begin{array}{l} 10^{23} = x \ln (10) \\ x = \frac{10^{23}}{\ln (10)} \\ x = 4.343 \times 10^{22} \\ e^{10^{23}} = 10^{(4.343 \times 10^{22})} . \end{array}$

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Write $e^{10^{23}}$ in the form $10^{x}$ , for some $x .$

Short Answer

Step by step solution

Step: 1 Using logarithmic function:

Step: 2 Finding value in form:

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Write e1023in the form 10x, for somex.

Short Answer

Step by step solution

Step: 1 Using logarithmic function:

Step: 2 Finding value in form:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electrostatics

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Study anywhere. Anytime. Across all devices.

Write $e^{10^{23}}$ in the form $10^{x}$ , for some $x .$