Question

HELP Needed With # 2 & 4
#2 Take the log of both sides
(x-1)log5 = x log 3
(x-1)0.698970004 = 0.477121255x ... now solve for x

#4 check your arithmetic after you distributed
(x-4)1.204119983=(3-x).477121254
1.204119983x - 4.816479931 = 1.431363764 -.4771212547x

x = ?
HELP ME PLEASE !

Answer 1

http://www.youtube.com/watch?v=IIDTlgvo0DM

Answer 2

#2:
Ok, so you had the equation:
\[5^{x-1}=3^x\]
What they were asking and partially did is to solve for x

So you take the log of both sides:
\[log_{10}(5^{x-1})=log_{10}(3^x)\]
And since \(\{log_a(b^c)=c\phantom{.}log_a(b)\}\), you obtain the following equation:
\[(x-1)log_{10}(5)=xlog_{10}(3)\]
Now you can distribute the left side to look like:
\[xlog_{10}(5)-log_{10}(5)=xlog_{10}(3)\]
And you gather "like" terms:
\[xlog_{10}(5)-xlog_{10}(3)=log_{10}(5)\]
Factor out an x:
\[x\big(log_{10}(5)-log_{10}(3)\big)=log_{10}(5)\]
And simplify since we know that \(\{log_c(a)-log_c(b)=log_c\left(\frac{a}{b}\right)\}\)
\[x\Bigg(log_{10}\left(\frac{5}{3}\right)\Bigg)=log_{10}(5)\]
And isolate for \(x\):
\[x=\frac{log_{10}(5)}{log_{10}\left(\frac{5}{3}\right)}\dot{=}\phantom{0}3.15\]