How do I solve this logarithmic equation?

Question

(1/4)Log base 7 of (8) - (1/4)Log base 7 of (25)

Answer 1

Let log be log to base 7 in the following :-

(1/4) log 8 - (1/4) log 25
log 8^(1/4) - log 25^(1/4)
log [ 8^(1/4) / 25^(1/4) ]
log [√2 / √5 ]
log [(1/5)√10 ]

Answer 2

First Convert the log base to 10

log(7)8 = log(10)8/log(10)7

log(7)25 = log(10)25/log(10)7

So
(1/4)log(7)8 = (3/4)log(10)2/log(10)7

(1/4)log(7)25 = (2/4)log(10)5/log(10)7

(1/4)log(7)8 = (3/4)0.30103/0.84510= 3 x 0.30103/4x0.84510
= 2.70927/3.3804= 0.80146

&
(1/4)log(7)25 = 2 x 0.69897/4 x 0.84510
= 1.39794/3.3804 = 0.41354
(1/4)log(7)8 - (1/4)log(7)25 = 0.80146 - 0.41354 = 0.38792

log(10)x = 0.38792 => x = 10^0.0.38792 = 2.44298

Answer 3

minus also means divide so put log base 7 8 on top and the other log under it and cancel the 1/4 out then you can cancel the log base 7 out and it will be 8/25

Answer 4

1/4Log(base 7)8 - 1/4Log( base 7)(25)
1/4Log( base 7)8/25
Log (base 7)(6/25)^1/4
=-0.1463883473