What is 2 log x - logy - 2 log z written as a single logarithm?

Mathematics

1 answer:

Hitman42 [59]3 years ago

4 0

Answer:

Log [x^2 / yz^2]

Step-by-step explanation:

2log(x) =log(x^2)

-log(y) = The minus sign means that you can divide it by first log(x^2)

-2log(z) =log(z^2), and the minus sign again means you can divide it by the first log(x^2)

So, the whole thing can be written like this:

Log(x^2) / [log(y)*log(z^2)], OR:

Log [x^2 / yz^2]

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Given f(x) = 2x - 1 and g(x) = x^2 + 3x - 1, find f(x) + g(x), f(x) - g(x), f(x) • g(x), and (f/g)(x)

lions [1.4K]

$\bf \begin{cases}
f(x)=2x-1\\
g(x)=x^2+3x-1
\end{cases}
\\\\[-0.35em]
\rule{34em}{0.25pt}\\\\
f(x)+g(x)\implies (2x-1)+(x^2+3x-1)\implies 2x+3x-1-1+x^2
\\\\\\
x^2+5x-2
\\\\[-0.35em]
~\dotfill$

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\\\\\\
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\\\\[-0.35em]
~\dotfill\\\\
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\\\\\\
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\\\\[-0.35em]
~\dotfill\\\\
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the division doesn't simplify any further.

5 0

2 years ago

A juice container is a square prism with base edge length 4 inches. When an 8-inch straw is inserted into the container as shown

aleksandrvk [35]

Assuming AB is the height because we are given it has a square base with 4 by 4

so draw a diagram ( see attachment)
given tha the 8 inch straw ha 1 inch sticking out, the diagonal is 7

use pythagorean theorem twice since 2 right triangles
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sqrt both sides
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the bottom diagonal is 4√2

bottom^2+height^2=7^2
(4√2)^2+(AB)^2=7^2
32+(AB)^2=47
minus 32 both sides
(AB)^2=15
sqrt both sides
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if AB is the height