Logarithm multiplication property error, can't figure out why. I know there is a mistake and where it is but I can't figure out why. Equation :3+2(12^(x+1))=291 From here I do: 2(12^(x+1))=291−3 2(12^(x+1))=288 Then I take the natural logarithms on both sides; ln(2∗12^(x+1))=ln(288) ln(2∗12^(x+1))=ln(2∗12^2) Now I apply multiplication property so ln(a∗b) should equal ln(a)+ln(b) But here it seems that I'm making a mistake, can't figure out why: ln(2)+ln(12^(x+1))=ln(2)+ln(12^2) subtract ln(2) on both sides: ln(12^(x+1))=ln(12^2) Then it should be: (x+1)ln(12)=2ln(12) x+1=2 x=1 but it's not the right result.. Thanks in advance :)

Cheyanne Jefferson

Cheyanne Jefferson

Answered question

2022-08-14

Logarithm multiplication property error, can't figure out why.
I know there is a mistake and where it is but I can't figure out why.
Equation:
3 + 2 ( 12 x + 1 ) = 291
From here I do:
2 ( 12 x + 1 ) = 291 3 2 ( 12 x + 1 ) = 288
Then I take the natural logarithms on both sides;
ln ( 2 12 x + 1 ) = ln ( 288 ) ln ( 2 12 x + 1 ) = ln ( 2 12 2 )
Now I apply multiplication property so ln ( a b ) should equal ln ( a ) + ln ( b ) But here it seems that I'm making a mistake, can't figure out why:
ln ( 2 ) + ln ( 12 x + 1 ) = ln ( 2 ) + ln ( 12 2 )
subtract ln ( 2 ) on both sides:
ln ( 12 x + 1 ) = ln ( 12 2 )
Then it should be:
( x + 1 ) ln ( 12 ) = 2 ln ( 12 ) x + 1 = 2 x = 1
but it's not the right result..
Thanks in advance :)

Answer & Explanation

datganuhl

datganuhl

Beginner2022-08-15Added 7 answers

The equation
3 + 2 12 x + 1 = 291
leads to
2 12 x + 1 = 291 3 = 288 12 x + 1 = 144 = 12 2
for which x + 1 = 2 by equating the exponents, or taking the logarithm of both sides. The value of x is x = 1

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