Posted by **jessica** on Saturday, February 16, 2013 at 7:29am.

if log x base a,log y base a and log z base a are three consecutive terms of an AP,show that x,y and z are consecutive terms of a GP

- math -
**Reiny**, Saturday, February 16, 2013 at 8:03am
let A = log_{a}x ---> x = a^A

let B = log_{a}y ---> y = a^B

let C = log_{a}z ---> z = a^C

but we are told that

log_{a}x , log_{a} y , and log_{a} z

form an arithmetic sequence

so A , B, and C form an arithmetic sequence

and B-A = C-B

do x, y, and z form a geometric sequence ?

if so , then y/x must equal z/y

y/x = a^B / a^A = a^(B-A)

z/y = a^C / a^B = a^(C-B)

but B-A = C-B. sp

y/x =z/y and x, y, z form a geometric sequence

## Answer This Question

## Related Questions

- Algebra 2 - -Explain the difference between log base b (mn) and ( log base b of ...
- Precalc - 1. 1/3log base 8 of (x+1)=2log base 8 of 3-(2/3)log base 8 of (x+1) 2...
- Advanced Functions/ Precalculus Log - 1. Evaluate 4^(log base4 64) + 10^(log100...
- Math - Help with these problems would be greatly appreciated: 1.Find the ...
- math - write as a single logarithm: -2logbase3(1/x)+(1/3)logbase3(square root of...
- math - Use the Laws of logarithms to rewrite the expression log(base 2)(11x(x-9...
- precalc - Solve: round to the thousandths if necessary! 1) 4^3/4x+5 = 12 2) log(...
- Trig - log base b 64 - log base b 16 = log base 4 16 solve for the variable.. i...
- precalc help - Find the exact value without a calc 1. log base 3 of 8 times log ...
- maths need help - If Log (a+3) (base 9) - log b(base 9)= c + (1/2) and log (a-3...

More Related Questions