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3 years ago

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

1 answer:

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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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 cater

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 ( $y=1$ ).