Question

Which equation is equivalent to 24% = 82-3?

0 24x _ 22x-3
O 24% = 22%-6
O 24% = 23x-3
O 24% – 23%-9

Answer 1

the 4th option

Explanation:

8 = 2³

so, when we convert

`{8}^(x - 3)`

into a "2 to the power of" expression, we get therefore

`({2}^(3)) ^(x - 3)`

and when we have an exponent of an exponent, we can simplify by multiplying these two exponents.

3×(x-3) = 3x - 9

and therefore we get

`{2}^(3x - 9)`

and by the way, we can now even easily solve this for x, as we know

`{2}^(4x) = {2}^(3x + x)`

after all, because 4x = x + x + x + x = 3x + x = ...

and because we got also

`{2}^(4x) = {2}^(3x - 9)`

we know that 3x + x = 3x - 9

and that gives us x = -9