Question 193789: Hello,
I have a problem with the following exponential equation, each time I try to solve it, I keep getting the wrong answer, could you look at my work and see what I am doing wrong? Thank you in advance.
Problem : 2^2x+4=3^x-21
This is what I have done so far :
ln(2)^2x+4=ln(3)^x-21
(2x+4)ln(2)= (x-21)ln(3)
2x*ln(2)+4*ln(2)=x*ln(3)-21*ln(3)
2x*ln(2)+x*ln(3)= -4*ln(2)-21*ln(3)
x(ln(3)+2*ln(2))=4*ln(2)-21*ln(3)
x= 4*ln(2)-21*ln(3)/ln(3)+2*ln(2)
Answer by RAY100(1637)   (Show Source):
You can put this solution on YOUR website! very good work
looking at line 4, the (+xln3) should be (-xln3)
,
we tried
(2x+4)ln2 = (x-21) ln3
,
(2x+4)= (ln3/ln2)(x-21) = 1.58496 ( x-21) = 1.58496 x - 33.284
,
.415 x = -37.284
,
x= (-89.8415) ANSWER
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checking
2^( 2(-89.8)+4) = 3^( (-89.4)-21)
2^-175.7 = 3^-110.84
1.3 x 10^-53 = 1.3 x 10^-53 ,,,ok
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Keep up the good work
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