For what value of a does (one-seventh) superscript 3 a + 3 baseline = 343 superscript a minus 1?
–1
0
1
no solution

  a = 0

Step-by-step explanation:

I find a graphing calculator useful for such questions. It shows the solution to be a = 0. For the graph, we have rewritten the equation from

  (1/7)^(3a+3) = 343^(a-1)

to

  (1/7)^(3x+3) -343^(x-1) = 0 . . . . . this graphing calculator likes x for the independent variable

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If you recognize that 343 is the cube of 7, you might solve this by taking logarithms to the base 7.

 (7^-1)^(3a+3) = (7^3)^(a-1)

Equating exponents of 7*, we get ...

  -(3a+3) = 3(a -1)

  -3a -3 = 3a -3 . . . . . eliminate parentheses

  0 = 6a . . . . . . . . . . . add 3+3a

  0 = a . . . . . . . . . . . . divide by 6

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* Equating exponents of 7 is the same as taking logarithms to the base 7. Here, we use the rules of exponents ...

  1/a^b = a^-b

  (a^b)^c = a^(bc)

1; 35 is the ratio

step-by-step explanation:

there are 70 more legs than eyes at the dog show (196 – 126 = 70). dogs have two more legs than eyes, and humans have the same number of legs as eyes. thus 70 is twice the number of dogs at the show, so the number of dogs is half of 70, which is 35. to get the number of humans, subtract 35 from 63: 63 – 35 = 28.

step-by-step explanation: