CPhill

Let's suppose that it is true....then, by a property of logs, we can wtite

log(ab) = log(a + b)

But, in general, ab ≠ a + b.  Thus, this "identity" isn't true.........

8x^2+2x-1=0    Let's see if we can factor this

(4x - 1) (2x + 1) = 0

Now, setting each factor to 0, we have

4x - 1 = 0   add 1 to both sides

4x = 1    divide by 4 on both sides

x = 1/4   and that's the first answer

And setting the other factor to 0, we have

2x + 1 =0      subtract 1 from both sides

2x = -1     divide by 2 on bith sides

x = -1/2    and that's the second answer

2(a-4)+15=13    simplify on the left

2a - 8 + 15 = 13

2a + 7 = 13   subtract 7 from both sides

2a = 6   divide by 2 on both sides

a = 3

Check

2(3-4) + 15 = 13

-2 + 15 = 13

13 = 13

6/81 = .074      the "074" repeats.......

In fact, 1 and -1 are the only two things that do work....!!!!

Notice that we could have also just multiplied 24.80 by 88% (.88) since she got a 12% discount, but NinjaDevo's method might be a little more informtive if we were also interested in the size of the discount...!!!

Our answers are correct, ND....

The calculator confirms it......

5(6 / 22 * 3 - 1)

$${\mathtt{5}}{\mathtt{\,\times\,}}\left({\frac{{\mathtt{6}}}{{\mathtt{22}}}}{\mathtt{\,\times\,}}{\mathtt{3}}{\mathtt{\,-\,}}{\mathtt{1}}\right) = {\mathtt{\,-\,}}{\frac{{\mathtt{10}}}{{\mathtt{11}}}} = -{\mathtt{0.909\: \!090\: \!909\: \!090\: \!909\: \!1}}$$

And besides, two great minds like ours can never be mistaken............LOL!!!!

Hit the "2nd" button on the on-site calculator.....you will see the "acos" button....this  is the same as cos^-1 ..... (i.e., the cosine inverse)

5[6 ÷ 22 · 3 - 1]    Remember that we perform any multiplications/divisions as we encounter them from left to right....so.....working inside the brackets first, we have

5[ (6/22)*(3) -1] =

5[(18/22) - 1] =

5[9/11 - 1] =

5[9/11 - 11/11] =

5 [-2/11] =

-10/11

4 · 1 - 32 ÷ 3  =

( 4 * 1 ) - ( 32 / 3) =

4 - (32 / 3) =

12/3 - 32/3 =

-20/3   or  -(6 + 2/3)