I don't know how to do these problems without guessing and checking. Will someone please help explain the reasoning to me? Thanks.
Find the value of "r" that makes each sentence true.
2^(r+5) = 2^(2r-1)
I know that the answer to this problem is r=6 but how??
also...
m^r / m^15 = (m^3)^r+2
(m^r) is in the numerator and (m^15) is in the denominator. also on the right side of the equation the 3,r, and 2 are all exponents.
For this problem I got that the answer was -8.5 and it works but the book got -10.5 (-21/2) and i couldn't even get this to equal both sides of the equation?? suggestions??
2007-09-10 10:49:38 · 7 answers · asked by Razzle Dazzle 3 in Science & Mathematics ➔ Mathematics
The first problem:
Since both sides have the same base, you can drop the base:
2^(r+5) = 2^(2r-1)
r + 5 = 2r - 1
r = 6
The second problem
m^r/m^15 = (m^3)^(r + 2)
Using the law of exponents
m^(r-15) = m^(3r + 6)
Using the same technique as above
r - 15 = 3r + 6
2r = -21
r = -21/2
2007-09-10 10:56:39 · answer #1 · answered by dr_no4458 4 · 0⤊ 1⤋
They have the same base, so the exponents must be equal.
r+5 = 2r - 1
on the second problem, again you have the same bases. Since the terms on the left are divided, the exponents are subtracted.
r - 15
on the right, a power is raised to a power, the exponents are multiplied 3r + 6
r-15 = 3r + 6
-21 = 2r
r = -21/2 = -10.5
2007-09-10 10:59:04 · answer #2 · answered by ccw 4 · 0⤊ 1⤋
If 2^x = 2^y then x=y
m^r / m^15 = m^(r-15)
(m^3)^(r +2) = m^(3^[r+2]) = m^(3r+6)
m^(r-15) = m^(3r+6)
r-15 = 3r+6
-21 = 2r
-21/2 = r = -10.5
2007-09-10 10:58:56 · answer #3 · answered by Raymond 7 · 0⤊ 1⤋
its as if saying r+5=2r-1 or r=6
2007-09-10 10:54:59 · answer #4 · answered by frozenlint 2 · 0⤊ 1⤋
The exponents must be equals
r+5 = 2r - 1
r = 6
Now the second one
m^(r-15) = m^[3(r+2)]
I want to believe that this 2 is not being added to (m+3)^r but to the exponent
r-15 = 3r + 6
2r = -21
r = -21/2
And your book is right.
Ana
2007-09-10 10:53:20 · answer #5 · answered by MathTutor 6 · 1⤊ 2⤋
2(r+5) = 2(2r-1)
2r+10 = 4r-2
-2r =-2r
0 + 10 = 2r -2
+2 +2
12 = 2r
-------------
2 2
answer is 12 divided by 2 = r
answer is 6=r
2007-09-10 11:05:29 · answer #6 · answered by meka g 6 · 0⤊ 1⤋
okay ill help with the first one. FIRST OF ALL. check if the bases are equal, which they are. they are both 2. if they werent, you would have to make them both equal. now just forget about the base and set the two powers together...
r + 5 = 2r - 1
----------------------
r + 6 = 2r
--------------------
6 = r
2007-09-10 10:58:42 · answer #7 · answered by Anonymous · 0⤊ 1⤋