The Student Room Group

Hard C2 logarithms question

Hi, last question in the excercise cant do. Will rep anyone who can clearly explain each step they did and why because i have the answers at the back:

a) Given that 3 + 2log2x = log2y, show that y=8x^2 (The 2 is a small 2 representing the base in each case.

b) Hence or otherwise, find the roots (alpha) and (beta) where alpha<beta, of the equation 3 + 2log2x = log2(14x-3) Again the 2 is small on both.

c) Show that log2alpha = -2

d) Calculate log2beta, giving your answer to 3 sig figs.

Thanks in advance,

Regards, Asad
Reply 1
a) 3 + 2log2x = log2y,
3log2 2 +2log2x = log2 8 + log2 x^2 = log2 8x^2

log2 8x^2 = log2 y
8x^2 = y
Reply 2
a) 3+2log2x=log2y
3+log2x^2=log2y
3=log2y-log2x^2
3=log2(y/x^2)
2^3=y/x^2
8=y/x^2
8x^2=y

b) 3 + 2log2x = log2(14x-3)
From the previous result you know that y=8x^2 and in this case, "y" = 14x-3 (if you compare with equation from a)
therefore 14x-3=8x^2
8x^2-14x+3=0
(4x-1)(2x-3)=0
x=1/4 or 3/2
therefore alpha=1/4 and beta=3/2

c) log2alpha=log2(1/4)
=log10(1/4)/log10(2)
=-2 --> using a calculator)
(I'm sure there's a neater way of doing this but can't think how sorry)

d) log2beta=log2(3/2)
=log10(3/2)/log10(2)
=0.585

I can't guarentee that they're right but hope it helps!
Reply 3
asadtamimi
Hi, last question in the excercise cant do. Will rep anyone who can clearly explain each step they did and why because i have the answers at the back:

a) Given that 3 + 2log2x = log2y, show that y=8x^2 (The 2 is a small 2 representing the base in each case.

b) Hence or otherwise, find the roots (alpha) and (beta) where alpha<beta, of the equation 3 + 2log2x = log2(14x-3) Again the 2 is small on both.

c) Show that log2alpha = -2

d) Calculate log2beta, giving your answer to 3 sig figs.

Thanks in advance,

Regards, Asad


(a) 3 + 2log2x = log2y, show that y=8x^2 (The 2 is a small 2 representing the base in each case.
= log28 + 2log2x=log2y
= 8+x^2=y...correct me but u wrote y=8x^2 ?!?!? i may be wrongtho.:frown:
(b) 14x-3= 8x^2therefore using the quadratic formula ,.....(14+or-root100)/16......you wud get a=1/4 and b=1.5.
(c) log 2 0.25 = -2 because 2^-2=1/4 !!!!
(d) log 2 1.5 = x, hence 2^x=1.5, hence xln2=ln1.5, therefore x= ln (1.5/2) = 0.585 (3sf)

i cant get A right, but rep please? lol
Reply 4
g_sachs, for a) when adding logs of the same base you can multiply them together under the same base .
Reply 5
arktos
g_sachs, for a) when adding logs of the same base you can multiply them together under the same base .


ye :smile: thanks, been 1 yr since i did c4, let alone c2.
Reply 6
I repped g_sachs but thanks arktos and especially piggy because piggy's working out is very clear to understand and now i know where i went wrong