Given that 2log2(x+15) -log2(x) = 6, show that x^2-34x+225=0

As we know nlog(a) is the same as log(a)^n, we can rearrange the equation to log2(x+15)^2 -log2(x) = 6. Also, we know that log(a) - log(b) is equal to log(a/b), so we can further rearrange the equation to log2((x+15)^2)/x) = 6. Another law of logarithms states to find a, when logx(a) = b , a = x^b. Thus, the equation becomes ((x+15)^2)/x) = 2^6Now we can simplify this equation. Opening the brackets of the numerator gives us x^2 +30x +225, all of which is divisible by x. 2^6 = 64. Because (x^2 +30x +225)/x = 64 we can multiply everything by x, giving us x^2 +30x +225 = 64xNow to rearrange it in the format the question asks, we can take 64x away from both sides, leaving us with x^2 -34x +225 = 0

RA
Answered by Rafey A. Maths tutor

11268 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

A curve has the equation 2x^2 + xy - y^2 +18 = 0. (1) Find the coordinates of the points where the tangent to the curve is parallel to the x-axis.


(A-Level) Find the coordinate of the stationary point of the curve y = 2x + 27/x^2


Solve the simultaneous equations: ...


How do you integrate ln(x) with respect to x?


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences