Log4 6+ 2 log4 7 how to get log4 294 when combining?

2log₄(7) = log₄(7²) = log₄(49)

log₄(6) + log₄(49) = log₄(6×49) = log₄(294)

2log4 7=log 4 7^2

log4 6 + log4 49=log4 294

When you add logs you would multiply the 6 and the 49.

let log be log base 4

log 6 + 2 log 7

log 6 + log 7²

log 6 + log 49

log 294

One basic rule of logs:

log of product = add the logs

log(ab) = log(a) + log(b)

(as long as they are both in the same base, of course).

Because the equal sign does not care which way you go, this works both ways.

Begin with

2*log4(7)

this is the same as

log4(7) + log4(7)

We are adding two logs in base 4, therefore we can replace with the log of multiplication:

2*log4(7) = log4(7) + log4(7) = log4(7*7) = log4(7^2) = log4(49)

All these things are the same value.

Many people use this shortcut:

the coefficient (in front of the log) becomes a power inside the log:

2*log4(7) = log4(7^2)

(the "2" in front, becomes a power inside)

Next, you add to that another log in base 4

log4(6) + 2*log4(7)

has already been changed to

log4(6) + log4(49)

Apply the same rule (adding logs = log of product):

log4(6*49) = log4(294)