Question

Evaluate: log7 14+log3 81+log4 1-log7 2

Answer 1

\(\Large\color{red}{ \bf log_{7}14 + log_{3}81+log_{4}1-log_{7}2 }\) like this ?

Answer 2

yes

Answer 3

I am going to be posting each step to give you time to process.\(\Large\color{red}{ \bf log_{7}(7 \times 2) + log_{3}81+log_{4}1-log_{7}2 }\)

Answer 4

\(\Large\color{red}{ \bf log_{7}(7) +log_{7}(2) + log_{3}81+log_{4}1-log_{7}2 }\)

Answer 5

\(\Large\color{red}{ \bf 1 +log_{7}(2) + log_{3}81+log_{4}1-log_{7}2 }\)

Answer 6

\(\Large\color{red}{ \bf 1 +log_{7}(2) + log_{3}(3^{4})+log_{4}1-log_{7}2 }\)

Answer 7

\(\Large\color{red}{ \bf 1 +log_{7}(2) + 4(log_{3}3)+log_{4}1-log_{7}2 }\)

\(\Large\color{red}{ \bf 1 +log_{7}(2) + 4(1)+log_{4}1-log_{7}2 }\)

\(\Large\color{red}{ \bf 1 +log_{7}(2) + 4+log_{4}1-log_{7}2 }\)

\(\Large\color{red}{ \bf 5 +log_{7}(2) +log_{4}1-log_{7}2 }\)

Answer 8

you have log_7 2 one positive and one negative, so they cancel.

\(\Large\color{red}{ \bf 5 +log_{7}(2) +log_{4}1-log_{7}2 }\)
turns into

\(\Large\color{red}{ \bf 5 +log_{4}1 }\)

Answer 9

So it is approximately just 5.

Answer 10

Wow that's insane but I love it :) thanks you've been a wonderful help

Answer 11

anytime !

Answer 12

I do have one more if you wouldn't mind...

Answer 13

Determine f^-1(3) if f(x)=7/x+4