If log2 base7 is 0.3562,log3 base7 is 0.5646 and log 5 base 7 is 0.8271 evaluate log30 base7
1.7479
This rule applies to logarithms with any base.
log ( a • b ) = log ( a ) + log ( b )
so
log ( a • b • c ) =
log ( a ) + log ( b ) + log ( c )
30 = 2 • 3 • 5
log₇ ( 30 ) = log ₇ ( 2 • 3 • 5 ) =
log₇ ( 2 ) + log₇ ( 3 ) + log₇ ( 5 ) =
0.3562 + 0.5646 + 0.8271 = 1.7479