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Irina18 [472]
3 years ago
7

ln(y+1)-lny=1+3lnx . Express y in terms of x, in a form not involving logarithms. (4 marks, Maths CIE A level)

Mathematics
2 answers:
Delicious77 [7]3 years ago
6 0
remember
ln(x)=log_e(x)
and
log_x(a)-log_x(b)= log_x( \frac{a}{b} )
and
log_a(b)=c means a^c=b
and
blog(a)=log(a^b)



so

ln(y+1)-ln(y)=1+3ln(x)
ln( \frac{y+1}{y} )=1+ln(x^3)

minus ln(x^3) from both sides

ln( \frac{y+1}{y}-ln(x^3) )=1
ln( \frac{y+1}{yx^3})=1
log_e( \frac{y+1}{yx^3})=1

translate

e^1=\frac{y+1}{yx^3}
e=\frac{y+1}{yx^3}

times both sides by yx^3

eyx^3=y+1

minus y from both sides

eyx^3-y=1
y(ex^3-1)=1

divide both sides by (ex³-1)

y= \frac{1}{ex^3-1}
True [87]3 years ago
6 0
Ln(y+1)-Lny=1+3 Lnx
ln \frac{y+1}{y} =lne+ln x^{3} 
ln \frac{y+1}{y} =ln e x^3,
 \frac{y+1}{y} =ex^3,
1+ \frac{1}{y} =e x^3,
 \frac{1}{y} =ex^3-1,

y= \frac{1}{e x^{3} -1}
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