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vovangra [49]
3 years ago
6

Explain how solve 4x + 3 = 7 using the change of base formula log base b of y equals log y over log b. Include the solution for

x in your answer. Round your answer to the nearest thousandth. ANSWER ASAP PLEASE
Mathematics
1 answer:
kvasek [131]3 years ago
8 0
Answer:
x=1
Step-by-step explanation:
Given is an exponential equation

Subtract 3 from both the sides
We get

Taking log

=1
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Use an induction proof to prove this statement:<br> For n≥1, 4^n+5 is divisible by 3.
Tpy6a [65]

Answer:

See below

Step-by-step explanation:

We shall prove that for all n\in\mathbb{N},3|(4^n+5). This tells us that 3 divides 4^n+5 with a remainder of zero.

If we let n=1, then we have 4^{1}+5=9, and evidently, 9|3.

Assume that 4^n+5 is divisible by 3 for n=k, k\in\mathbb{N}. Then, by this assumption, 3|(4^n+5)\Rightarrow4^k+5=3m,\: m\in\mathbb{Z}.

Now, let n=k+1. Then:

4^{k+1}+5=4^k\cdot4+5\\=4^k(3+1)+5\\=3\cdot4^k+4^k+5\\=3\cdot4^k+3m\\=3(4^k+m)

Since 3|(4^k+m), we may conclude, by the axiom of induction, that the property holds for all n\in\mathbb{N}.

3 0
2 years ago
In the figure below,
bogdanovich [222]

Answer:

b

Step-by-step explanation:

8 0
3 years ago
candy bars are sold at a local store for 60 cents each. The factory has $1000 in fixed costs plus 10 cents of additional expense
Westkost [7]

Answer:

2000 bars, or $1200

Explanation:

Let x represent the number of candy bars that are sold.  Since they are sold for $0.60 each, this gives us the expression

0.60x

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The factor has $0.10 per candy bar additional expense; this gives us the expression

0.10x.

However the factory also has $1000 fixed costs; this gives us

0.10x + 1000

to represent the costs.

The break-even point is the point where these two expressions are equal; this gives us the equation

0.60x = 0.10x + 1000

Subtract 0.10x from each side:

0.60x - 0.10x = 0.10x + 1000 - 0.10x

0.50x = 1000

Divide both sides by 0.50:

0.50x/0.50 = 1000/0.50

x = 2000

The break-even point is 2000 candy bars, which would sell for

0.60(2000) = $1200

3 0
3 years ago
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The ratio of yellow to total is 2 to 8, or 1:4 if you divide both by 2. So the answer is B.
7 0
2 years ago
0.8 hectometers = what millimeters
Rus_ich [418]

Answer:

Ummmm I Cannot remember use your caculator

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3 years ago
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