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Chapter 15: Problem 137

Without using a calculator, what is the base- 10 logarithm of \(10^{-34}\) ?

Short Answer

Expert verified
The base-10 logarithm of \(10^{-34}\) is \(-34\).

Step by step solution

01

Recall the properties of logarithms

Recall that the base-10 logarithm is expressed as \(\log_{10}\) and follows this rule: \[\log_{10}(a^b) = b \cdot \log_{10}(a)\]
02

Apply the logarithm rule

Use the logarithm rule mentioned above to find the base-10 logarithm of \(10^{-34}\): \[\log_{10}(10^{-34}) = (-34) \cdot \log_{10}(10)\]
03

Simplify the expression

Now, we know that \(\log_{10}(10) = 1\), as any base logarithm of that base is always equal to 1: \[\log_{10}(10) = 1\] So, we can simplify the expression: \((-34) \cdot \log_{10}(10) = (-34) \cdot 1\)
04

Calculate the result

Finally, we can calculate the result: \(-34 \cdot 1 = -34\) Therefore, the base-10 logarithm of \(10^{-34}\) is \(-34\).

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Most popular questions from this chapter

Sulfuric acid, \(\mathrm{H}_{2} \mathrm{SO}_{4}\), is a diprotic acid with dissociation equilibrium constants of \(K_{\mathrm{eq}}>1.0 \times 10^{3}\) and \(K_{\mathrm{eq}}=1.2 \times 10^{-2} .\) Write the two dissociation equilibrium equations, and match the proper \(K_{\text {eq }}\) to each. Which species is the weak acid?

Knowing that aniline (Problem \(15.158\) ) is a weak base, is its conjugate acid a weak acid or a strong acid?

What is the \(\mathrm{pH}\) of a solution whose \(\mathrm{OH}^{-}\) concentration is \(10^{-14} \mathrm{M} ?\) Is the solution acidic or basic?

Amines are organic compounds that contain an \(\mathrm{NH}_{2}\) group, and water-soluble amines are weak bases in water. For example, the compound methylamine, \(\mathrm{H}_{3} \mathrm{C}-\mathrm{NH}_{2}\), is a weak base. (a) Draw a dot diagram for methylamine. (b) Using dot diagrams, show the equilibrium reaction between methylamine and water. (c) To which side does the equilibrium in part (b) lie? What did we tell you that allowed you to figure out the answer? (d) The similar compound ethane, \(\mathrm{H}_{3} \mathrm{C}-\mathrm{CH}_{3}\), does not act as a weak base. Why can methylamine act as a weak base but \(\mathrm{H}_{3} \mathrm{C}-\mathrm{CH}_{3}\) can't? (Hint: Draw a dot diagram for \(\mathrm{H}_{3} \mathrm{C}-\mathrm{CH}_{3}\).) (e) Is it appropriate to call methylamine an electrolyte? If so, is it weak or strong? Explain.

Classify each substance as strong electrolyte, weak electrolyte, or nonelectrolyte: (a) \(\mathrm{CH}_{3} \mathrm{COOH}\) (b) \(\mathrm{KCH}_{3} \mathrm{COO}\) (c) \(\mathrm{H}_{2} \mathrm{SO}_{4}\) (d) \(\mathrm{CH}_{2} \mathrm{Cl}_{2}\) (e) \(\mathrm{NH}_{3}\) (f) \(\mathrm{H}_{3} \mathrm{PO}_{4}\) (g) \(\mathrm{ZnSO}_{4}\)
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