Question

Log 448 equal to 6 log 2 + log 7

Answer 1

$\underline{\textbf{To prove:}}$

$\mathsf{\log\,448=6\,\log\,2+\log\,7}$

$\underline{\textbf{Solution:}}$

$\underline{\textsf{Formula used:}}$

$\mathsf{(1)\;\log_aM^n=n\,\log_aM}$

$\mathsf{(2)\;\log_a(MN)=\log_aM+\log_aN}$

$\mathsf{Consider,}$

$\mathsf{6\,\log\,2+\log\,7}$

$\mathsf{Using\;formula\;(1)}$

$\mathsf{=\log\,2^6+\log\,7}$

$\mathsf{=\log\,64+\log\,7}$

$\mathsf{Using\;formula\;(2)}$

$\mathsf{=\log(64{\times}7)}$

$\mathsf{=\log\,448}$

$\implies\boxed{\mathsf{\log\,448=6\,\log\,2+\log\,7}}$

$\underline{\textbf{Find more:}}$

x^2 + y^2= 25xy, then prove that 2 log(x+y)=3log3+logx+logy

https://brainly.in/question/477579  

If 2log(x-y)=logx +logy, prove that 2log(x+y)= log5+logx +logy

https://brainly.in/question/16912979