Question 421618
Show that log(8- base) 1000 = log (2- base) 10 algebraically.

..

log8(1000)=x
log2(10)=x
convert both equations to exponential form. The base raised to the logarithm of the number is equal to the number.
8^x=1000
(2^3)^x=1000
2^3x=1000
..
2^x=10
cube both sides
(2^x)^3=10^3
2^3x=1000

ans: equations therefore are algebraically equal to each other.