Prove that log(a) b = 1/(log(b) a)
- print Print
- list Cite
Expert Answers
justaguide
| Certified Educator
calendarEducator since 2010
write12,544 answers
starTop subjects are Math, Science, and Business
We have to prove that `log_a b = 1/(log_b a)`
Use the property for changing the base of logarithms: `log_a b = (log_c b)/(log_c a)`
Change the base of `log_a b` to b
`log_a b = (log_b b)/(log_b a)`
Use the property: `log_b b = 1`
=> `1/(log_b a)`
This proves that `log_a b = 1/(log_b a)`
Related Questions
- If log a = 35 and log b= 20 calculate : log (ab) , log (a/b) , log (1/a) and log (1/b)
- 2 Educator Answers
- Using properties of determinant prove that `|[1, a, a^2],[1, b, b^2],[1, c, c^2]| = (a-b)(b-c)(c-a)`
- 1 Educator Answer
- If x = log[a]bc y = log[b]ca z = log[c]ab ptove that x+y+z+2 = xyz
- 1 Educator Answer
- Prove that log(a*b) = log a + log b
- 1 Educator Answer
- if a^x=b^y=c^z and b^2=ac Prove that, 1/x+1/z=2/y.
- 1 Educator Answer