Math: More about logs

Understanding logs is critical to anyone who needs to pass math 12 precalculus.  Your tutor will give you a new point of view about them.

Imagine you have this equation:

(1)   \begin{equation*}3^x=46\end{equation*}

The solution is

(2)   \begin{equation*}x=\frac{log46}{log3}\end{equation*}

Now let’s evaluate the decimal using a calculator:

(3)   \begin{equation*}\frac{log46}{log3}=3.4850\end{equation*}

(We have rounded to four decimal places.)

Next, let’s check our answer by plugging it into the original equation. In order to raise 3 to the exponent of 3.4850, you’ll likely use the yx key or else the ^ key.

(4)   \begin{equation*}3^{3.4850}=46.0010\end{equation*}

Close enough:)  Usually, during calculations, four decimal places is sufficient. This is true not only for logarithms, but trig as well.

With the pressure of final exams behind us, we will continue to provide light reading throughout the summer.  We tutor all year:)

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

English: Punctuation with Quotation Marks

As term-end essays soon come due, your English tutor mentions a couple of finer details….

When quotation marks enclose speech, you put the comma or period inside:

“Call them back,” he requested.

“I’ll never make that mistake again.”

You also put the other punctuation inside, if it is part of what’s said:

“I love your car!”

“When will I get to drive it?”

What about if you have quotes around a title or saying?  For periods and commas, you do the same:

When my daughter told me my car was “sick,” I didn’t realize she was complimenting it.

Reading Amy Tan’s “Rules of the Game,” I developed a new appreciation for the importance of rules.

Tonight she will finish James Baldwin’s “Sonny’s Blues.”

Note, however, that other punctuation (that is not part of the saying or title) goes outside:

Tonight, will you finish “Sonny’s Blues”?

I just found out my car is “sick”!

Quotes are used around the titles above because they are short stories; if they were novels, they would be underlined or italicized.

We wish you the best of luck with all your term-end efforts:)

Source:  TRU Open Learning Writer’s Style Guide.  Open Learning Agency, 2003.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

English: Using conjunctive adverbs

When you tutor English, conjunctive adverbs come up – especially around due dates for important English compositions.

Following a semicolon, a conjunctive adverb can be used.  It leads to an attractive construction that can elevate your essay.

Their best pitcher was benched; nonetheless, they won the game.

I prefer pasta to meat; however, I really enjoyed your tacos.

In the above sentences, “nonetheless” and “however” are conjunctive adverbs.  In each case, the conjunctive adverb is placed after the semicolon.  The idea that follows – which must be a complete thought on its own – is rather surprising, given the idea that precedes the semicolon.

Conjunctive adverbs don’t have to lead to surprise.  Consider the following:

Put the cake in a preheated 350 degree oven; next, start the icing.

In the above sentence, “next” is a conjunctive adverb.

A conjunctive adverb is a word that links two ideas (hence, conjunctive), while describing a connection between the actions of each.  Often, the connection is irony: with however or nonetheless, the second idea seems surprising relative to the first. Likewise, the connection can be sequential – as with “next” – or cause-and-effect, as with “thus”.

Conjunctive adverbs can, of course, be used to begin sentences as well as after a semicolon.  Your English tutor encourages using them here and there in order to spice up your writing:)

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

English: Using they or their with a singular pronoun?

She-or-he and her-or-his are clumsy constructions.  Can you escape them?  The English tutor has looked it up to be sure….

Most writers face the situation commonly:

Leaving the shelter of the train, everyone put on ______ hat.

“Everyone” is, of course, singular.  If you knew the people were all women, you would love to say

Leaving the shelter of the train, everyone put on her hat.

What if the group is mixed – as usually it would be?

Leaving the shelter of the train, everyone put on her or his hat.

In today’s times, using “her or his” is the proper way.  Grammarwise, it’s correct because her or his, being singular, agrees with everyone.  Politically it’s correct, being gender-inclusive.  However, it complicates the sentence.

A common solution to the dilemma:

Leaving the shelter of the train, everyone put on their hats.

Can you actually get away with using their – which is plural – to refer to everyone, which is singular?  The answer depends on your context:  formal writing won’t let you. However, informal writing permits it.

In a world that seems increasingly informal, formal writing still has some strongholds.  An English professor likely won’t let you get away with using their in the situation we are discussing.

Here are some possible fixes that make formal writing a little more graceful:

Leaving the shelter of the train, everyone put on her/his hat.

Everybody realizes she/he needs to retrain.

Everybody realizes s/he needs to retrain.

Ask your professor what s/he will accept.  Remember:  when in doubt, go formal:)

Source:  McGraw-Hill Handbook of English, Fourth Canadian Edition, 1986.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.