Question

Chapter 5:Indices and Logarithms
Solve the following equation
@ganeshie8 @ikram002p

Answer 1

\[4^{n+3}=7^{n-1}\]

Answer 2

take natural log both sides

Answer 3

then use below logarithm property : \[\large \ln (a^{\color{red}{x}}) = \color{Red}{x}\times \ln (a)\]

Answer 4

\[\log _{10}4^{n+3}=\log _{10}7^{n-1}\]

Answer 5

\[(n+3)~\times~\log _{10}4=(n-1)~\times~\log _{10}7\]

Answer 6

what should we do next?

Answer 7

distribute..

Answer 8

\[(\color{Red}{n}+3)~\times~\log _{10}4=(\color{Red}{n}-1)~\times~\log _{10}7\]

\[\color{Red}{n}\log _{10}4 + 3\log _{10}4=\color{Red}{n}\log _{10}7- \log_{10} 7\]

Answer 9

collect terms with \(\color{Red}{n}\) on one side and factor \(\color{Red}{n}\)

Answer 10

\[n~\log _{10}4-n~\log _{10}7=-3\log _{10}4-\log _{10}7\]

Answer 11

\[n(\log _{10}4-\log _{10}7)=-3\log _{10}4-\log _{10}7\]

Answer 12

\[n =\frac{ -3\log _{10}4-\log _{10}7 }{ \log _{10}4-\log _{10}7 }\]

Answer 13

n=10.91

Answer 14

Yes!

Answer 15

Thnx @ganeshie8