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mihalych1998 [28]
2 years ago
11

Rewrite the following expression using the properties of logarithms. log2z+2log2x+4log9y+12log9x−2log2y

Mathematics
1 answer:
kramer2 years ago
5 0
Use the rules of logarithm:
1. log(x)+log(y)=log(xy)
    log(x)-log(y)=log(x/y)
2. k*log(x) = log(x^k)
    log(x)/k = log(x^(1/k))

<span>log(2z)+2log(2x)+4log(9y)+12log(9x)−2log(2y)
=</span>log(2z)+log(4x^2)+log(9^4y^4)+log(9^12x^12)−log(4y^2)
=log(2z)+log(4x^2)+log(6561y^4)+log(282429536481x^12)−log(4y^2)
=log(59296646043258912 * x^14 * y^6 * z)
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When 27x^2z/-3x^2z^6 is completely simplified, the exponent on the variable z is _____.
Savatey [412]
<span>The expression given (27x^2)z/(-3x^2)(z^6), can be simplify as below:

 By properties of powers, if you have the same base, you can substract the exponents. Then:

 =(</span>27x^2)z/(-3x^2)(z^6)
 =-9z/z^6  (As you can see: x^2-2= x^0=1)
 =-9/z^5    (Then, z^6-1=z^5)
<span>
 Therefore, the answer is: The exponent on the variable z is 5.</span> 
7 0
2 years ago
Adam is building a rectangular swimming pool. The perimeter of the pool must be no more than 120 feet. If the length of the pool
Orlov [11]

2(22 + w) \leq 120

22 + w \leq 60

w \leq 38

5 0
2 years ago
The surface area for a rectangular prism with a square base is SA=2s2+4shSA=2s2+4sh.
Rus_ich [418]
A=2s^2+2sh\implies A=2\times2^2+4\times2\times4=40
4 0
2 years ago
How many multiples of 2 are there between 99 and 999?
agasfer [191]

Answer:

Step-by-step explanation:

The multiples of numbers calculator will find 100 multiples of a positive integer. For example, the multiples of 3 are calculated 3x1, 3x2, 3x3, 3x4, 3x5, etc., which equal 3, 6, 9, 12, 15, etc. You can designate a minimum value to generate multiples greater than a number.

7 0
2 years ago
Sal conducted an online survey to find out which kind of music people like best. The circle graph displays the results. If 250 p
Serga [27]

Answer:

Hence, the total number of people who chose rap as their favorite kind of music is:

                             60 people

Step-by-step explanation:

The percentage of people who like different kind of music are given by:

    Music                   Percent

Rock 'n' Roll               28%

  Rap                          24%

Hip Hop                    20%

   Jazz                        18%

 Other                        10%

Total number of people who responded to survey=250

Hence, the number of people who chose rap as their favorite music is:

24% of 250

i.e. 24%×250

= 0.24×250

=60

        Hence, people who chose rap are:

                   60 people.

6 0
2 years ago
Read 2 more answers
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