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Ierofanga [76]
3 years ago
10

Given the exponential equation 3x = 243, what is the logarithmic form of the equation in base 10?

Mathematics
1 answer:
weeeeeb [17]3 years ago
6 0
The answer is x= \frac{log_{10} (243 )}{log_{10} (3 )}

3^{x} =243
Logarithm both sides of the equation:
log_{10} (3^{x} ) = log_{10} (243 )
Since: log (a^{b}) = b*log(a), then: log_{10} (3^{x} ) =x*log_{10} (3 )
Back to our equation:
log_{10} (3^{x} ) = log_{10} (243 ) \\ 
x*log_{10} (3 ) = log_{10} (243 ) \\ 
x= \frac{log_{10} (243 )}{log_{10} (3 )}



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n200080 [17]

Answer:

The number of pies does the baker have left is 15.

Step-by-step explanation:

Given : A baker made 20 pies. A Boy Scout troop buys one–fourth of his pies, a preschool teacher buys one–third of his pies, and a caterer buys one–sixth of his pies.

To find : How many pies does the baker have left?

Solution :

Let x be the number of pies does the baker have left.

According to question,

Number of pies buys,

One-fourth =\frac{1}{4}

One-third =\frac{1}{3}

One-sixth =\frac{1}{6}

i.e. x=20-(20\times \frac{1}{4}+20\times \frac{1}{3}+20\times \frac{1}{6})

x=20-(5+20\times \frac{1}{3}+10\times \frac{1}{3})

x=20-(5+\frac{20+10}{3})

x=20-(5+ \frac{30}{3})

x=20-(5+10)

x=20-(15)

x=5

The number of pies does the baker have left is 15.

7 0
3 years ago
Which set of ordered pairs could be generated by an exponential function?
klemol [59]

Answer: Third option.

Step-by-step explanation:

By definition, Exponential functions have the following form:

y = ab^x

Where "b" is the base (b > 0 and b\neq 1), "a" is a coefficient (a\neq 0) and "x" is the exponent.

 It is importat to remember that the "Zero exponent rule" states that  any base with an exponent of 0 is equal to 1.

Then, for an input value 0 (x=0) the output value (value of "y") of the set of ordered pairs that could be generated by an exponential function must be 1 (y=1).

You can observe in the Third option shown in the image that when x=0, y=1

 Therefore, the set of ordered pairs that could be generated by an exponential function is the set shown in the Third option.

4 0
3 years ago
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sattari [20]

Answer:

Is A supposed to be 6 x m or no??

Step-by-step explanation:

8 0
3 years ago
In triangle ABC, angle A is 25 degree, and Angle B is 105 degrees. what is the measure of angle c
Scilla [17]
Angle c= 60°

This is because 105+25+x=180°
Hope this helps and good luck!! :)
8 0
3 years ago
How does the graph of y=|x|+ 4 compare to the graph of the parent function y=|x|?​
neonofarm [45]

Answer:

Please check the explanation and attached graph.

Step-by-step explanation:

Given the parent function

y = |x|

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Given that the image function

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It is clear that h = 4. Since 4 > 0, thus the graph y=|x|+4 translated '4' units up.

The graph of both parent and translated function is attache below.

In the graph,

The blue line represents the parent function y=|x|.

The red line represents the image function y=|x| + 4.

It is clear from the graph that the y=|x| + 4  translated '4' units up.

Please check the attached graph.

3 0
3 years ago
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