Solve the given equations for x:
a). (e^(2x+3)) - 7 = 0
b). ln(5 - 2x) = -3
Any and all help is much appreciated! Thanks so much in advance!
a) Rearranging the terms, we obtain:
e^(2x + 3) = 7
Setting both sides by ln, and we have:
lne^(2x + 3) = ln(7)
2x + 3 = ln(7)
Then,
2x = ln(7) - 3
x = (ln(7) - 3)/2
b) ln(5 - 2x) = -3
Set both sides to the base of e.
e^(ln(5 - 2x)) = e^(-3)
5 - 2x = e^(-3)
-2x = e^(-3) - 5
x = (e^(-3) - 5)/-2
x = (5 + (1/e³))/2
I hope this helps!
With this, think approximately that something expanded by way of 0 turns into 0. With that stated, set each and each of those expressions in my opinion to 0. x-3 = 0 x = 3 2x+7 = 0 2x = -7 x = -7/2 x = -7/2, 3
(a) e^(2x+3) = 7 or 2x +3 = log7
or 2x = log7 --3
x = ( log7 -3)/2 = --1.07745 ans
(b) log (5-2x)= --3 or 10^-3 = 5 -2x [ log _a b = x then b = e^x ]
2x = 5 --1/1000 or x= ( 4999/2000) = 2.4995 ans
or alternate - 5--2x = antilog( --3 )
= atilog ( bar 3 ,0000) = .001
2x = 5 --.001 = 4.999 or x= 4.999/2 = 2.4995 ans
a. e^2x+3=7
ln7=2x+3
ln7-3/2=x or 2.91886
b. e^-3=5-2x
e^-3-5/-2=x or -2.4751
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Verified answer
a) Rearranging the terms, we obtain:
e^(2x + 3) = 7
Setting both sides by ln, and we have:
lne^(2x + 3) = ln(7)
2x + 3 = ln(7)
Then,
2x = ln(7) - 3
x = (ln(7) - 3)/2
b) ln(5 - 2x) = -3
Set both sides to the base of e.
e^(ln(5 - 2x)) = e^(-3)
5 - 2x = e^(-3)
Then,
-2x = e^(-3) - 5
x = (e^(-3) - 5)/-2
x = (5 + (1/e³))/2
I hope this helps!
With this, think approximately that something expanded by way of 0 turns into 0. With that stated, set each and each of those expressions in my opinion to 0. x-3 = 0 x = 3 2x+7 = 0 2x = -7 x = -7/2 x = -7/2, 3
(a) e^(2x+3) = 7 or 2x +3 = log7
or 2x = log7 --3
x = ( log7 -3)/2 = --1.07745 ans
(b) log (5-2x)= --3 or 10^-3 = 5 -2x [ log _a b = x then b = e^x ]
2x = 5 --1/1000 or x= ( 4999/2000) = 2.4995 ans
or alternate - 5--2x = antilog( --3 )
= atilog ( bar 3 ,0000) = .001
2x = 5 --.001 = 4.999 or x= 4.999/2 = 2.4995 ans
a. e^2x+3=7
ln7=2x+3
ln7-3/2=x or 2.91886
b. e^-3=5-2x
e^-3-5/-2=x or -2.4751