Logarithm

[Barbie]

2 (i) Show that the equation log2(x + 5) = 5 − log2 x
can be written as a quadratic equation in x. (ii) Hence solve the equation
log2(x + 5) = 5 − log2 x

 

[Dr.Peterson]

Presumably the 2's are meant to be subscripts, so the equation is log₂(x + 5) = 5 − log₂ x .

What have you tried in order to do part (i)? Did you add log₂ x to both sides, and combine them into one?

 

[Kaza]

log₂(x+5)=log₂(2⁵)-log₂(x)=log₂(2⁵/x)
x+5=2⁵/x

 

[Dr.Peterson]

That's a good beginning.

Now, try solving x + 5 = 32/x. I would first clear fractions by multiplying by x.

 

[Steven G]

Please remember that when you solve x + 5 = 32/x there are some restrictions on x. Can you state the restrictions on x?

 

[pka]

2 (i) Show that the equation\(\displaystyle \log_2(x + 5) = 5 − \log_2( x)\)
can be written as a quadratic equation in x.
(ii) Hence solve the equation
\(\displaystyle \log_2(x + 5) = 5 − \log_2( x)\)

\(\displaystyle \log_2(x + 5) = 5 − \log_2( x)\\
\log_2(x + 5)+ \log_2( x) = 5\\
\log_2[(x + 5)(x)] = 5\\
x^2+5x=2^5\)
Can you follow that and finish?