Question

if log 8=0.9030 and log 9=0.9542 then the value of log 512 to the base 5 is​

Answer 1

Answer:

log₅512  = 3.876

Step-by-step explanation:

log₅512  = log 512 / log 5

= log (8³)/ log 5

= 3 log 8 / log (10/2)

= 3 log 8 / (log 10 - log 2)

= 3 log 8 / ( 1 - log 2)

log 8=0.9030

=> log 2³ = 0.9030

=> 3 log 2 = 0.9030

=> log 2 = 0.3010

= 3 * 0.9030 / (1 - 0.3010)

= 3 * 0.9030 / (0.6990)

= 3.8755

= 3.876

log₅512  = 3.876