Pleas help with my homework?

Question

I need help solving the following equation thanks:
ps. can you show me step by step please

5^x=4^(x+1)

Answer 1

Noooooooooooooooo do it yourself

Answer 2

to do this you are going to have to take the natural log, or ln or each function.

You want to do this because with the properties of natural logs, you can move exponents to the front of the function. ( For example: 3^x=xln3)

To take the ln of a equation, you must do so to both sides, so

5^x=4^(x+1)
becomes
ln5^x=ln4^(x+1)
now, due to the propetry that allows you to bring the exponents down in front
xln5=(x+1)ln4
expand
xln5=xln4+ln4
get all the x's on one side
xln5-xln4=ln4
pull out an x
x(ln5-ln4)=ln4
solve for x
x=ln4/(ln5-ln4)

The end!

Answer 3

Convert both sides to log form:
x*log 5=(x+1)*log4 then look up bse 10 logs of 4 and 5 and substitute logs into the equation:
.69897*x =.60206*(x+1)
Simplify: .69897*x = .60206*x +1*.60206
Collect terms: (.69897 -.60206)x = .60206
Therefore: .09691*x =.60206
And: x = 6.212568....

Answer 4

Taking log of both sides

xlog5 =(x+1)log 4 so x(log 5-log4) = log4 but log5-log4=
=log(5/4)

so x= (log4)/log(5/4)=6.2126

Answer 5

5^x=4^(x+1) take the ln of both sides remembering that
ln a^b=b ln a

x ln 5=(x+1) ln 4=x ln 4 + ln 4 subtract x ln 4 from each side
x ln 5 - x ln 4=ln 4 factor out x in LHS & use ln a - ln b=ln (a/b)
x(ln 5-ln 4)= ln 4
x(ln (5/4))=ln 4 divide both sides by ln (5/4)
x=ln 5 /ln (5/4)=7.21567

Answer 6

5^x=4^(x+1)
log 5^x = log 4^(x+1)
x log 5 = (x+1)log 4
x/(x+1) = log 4/log 5 = .861
x = .861(x+1) = .861x + .861
x - .861x = .861
.139x = .861
x = .861/.139 = 6.19

Answer 7

5^x=4^(x+1)
5^x = 4^x * 4
x ln 5 = x ln 4 + ln 4
x (ln 5 - ln 4) = ln 4
x = ln 4 / (ln 5 - ln 4)
x = 6.21

Answer 8

its easy

u need the numbers on the bottom to be the same

then u can make x = x+1

Answer 9

x log (5) = (x+1) log 4

xlog(5) - x log(4) = log(4)

x (log5 - log4) = log4

x = (log4)/(log 5 -log4)

Answer 10

taking log on both sides,

xlog5=(x+1)log4

(x)/(x+1)=log4/log5