Answers

The Brainliest Answer!
2015-04-01T03:07:06+05:30

This Is a Certified Answer

×
Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
74
f(x)=\frac{1+x}{1-x}\\\\f(\frac{2x}{1+x^2})=Log[\frac{1+\frac{2x}{1+x^2}}{1-\frac{2x}{1+x^2}}]\\\\=Log[\frac{(1+x)^2}{(1-x)^2}]\\\\=2Log[\frac{1+x}{1-x}]=2f(x)\\
===============================
75.
let\ k=(x-y)Log_a\ 3=(y-z)log_b\ 3=(z-x)log_c\ 3\\\\\frac{x-y}{k}+\frac{y-z}{k}+\frac{z-x}{k}=\frac{1}{Log_a\ 3}+\frac{1}{Log_b\ 3}+\frac{1}{Log_c\ 3}\\\\0=Log_3\ a+log_3\ b+log_3\ c\\\\0=Log_3\ abc\\\\abc=3^0=1\\\\=>5^{abc}=5
====================================
76.
x = log_a\ bc=log_ab+log_ac;\\y=Log_b\ ca=Log_bc+Log_ba;\\z = log_c\ ab=log_ca+log_cb\\\\xy=(log_ab+log_ac)(Log_bc+Log_ba)\\.\ \ =log_ab\ Log_bc+1+Log_ac\ Log_bc+log_ba\ log_ac\\.\ \ =Log_ac+1+Log_ac\ Log_bc+Log_bc\\\\xyz=(1+Log_ac+Log_ac\ Log_bc+Log_bc)(log_ca+log_cb)\\.\ \ \ =log_ca+log_cb+1+Log_ab+Log_bc+Log_ac+Log_ba+1\\.\ \ \ =2+log_c\ ab+log_a\ bc+log_b\ ac\\.\ \ \ =2+x+y+z

=======================
77.
log_4(x-1)=Log_2(x-3)=k\\\\x-1=4^k=2^{2k}=(2^k)^2\\x-3=2^k\\\\x-1=(x-3)^2\\=>x^2-7x+10=0\\=>as\ discriminant=7^2-4*10>0,there\ are2\ solutions
====================================
78.    x ≠ π/2 or π  as log cos x  and log sin 2x exist.

let\ Log_{0.1}\ Sin2x=z\\Sin2x=0.1^z=10^{-z}\\z=-Log_{10}\ Sin2x\\\\Log_{0.1}\ Sin2x +log_{10}\ cosx=log_{10}\ \frac{1}{\sqrt3}\\\\-Log_{10}\ sin2x+log_{10}\ cosx=log_{10}\ \frac{1}{\sqrt3}\\\\Log_{10}\ cos\ x/Sin\ 2x=log_{10}\ \frac{1}{\sqrt3}\\\\\frac{1}{2sin\ x}=\frac{1}{\sqrt3}\\\\x=sin^{-1}\sqrt3/2=\pi/3

2 5 2
thanks
sir sir plz
plz
xplain 76 one
how did you multiply xy