Verified answer

i presume you mean log base 6 of 42 - log base 6 of 7 ?

log6 42 - log6 7

= log6 (6*7) - log6 7

log laws tell us log(a*b) = log(a) + log(b)

= log6 6 + log6 7 - log6 7

= log6 6

= 1

since ,

we Know

log a^b = b log a

Therefore,

log6^42= 42log 6...(1)

log6^7= 7log6...(2)

Subtracting (2) from (1)

we get,

log6^42 - log6^7

= 42 log 6 - 7 log 6

= 35 log 6

=log 6^ 35

=27.235

log6^42 - log6^7 what do you want? a simplified expression?

by a log law which you have to search up if your not familiar with

→ log(6^42 / 6^7)

→ log(6^35)

→ 35log6

→ ____ if you want a numerical answer.

log(base) value

log (6) 42 = log(6) [7*6] = log(6) 7 +log(6) 6

so we have log(6) 7 +log(6) 6 - log(6) 7 = log(6) 6 which is equal 1

log^42-log^7=42log6-7log6=log6[42-7]