Help With Logarithm Questions?

Question

Can you please solve for x and explain (show you work step by step) how you did questions 9, 10, 11, and 12. Please write your final answer in 3 significant figures.

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Answer 1 · 2017-05-03T13:23:38

Solution to question 9

#x~~4.42# to 2 decimal places.

9) #" "2^(x+1)=3^(x-1)#

Take logs of both sides

#ln(2^(x+1))=ln(3^(x-1))#

#(x+1)ln(2)=(x-1)ln(3)#

#xln(2)+ln(2)=xln(3)-ln(3)#

#xln(3)-xln(2)=ln(2)+ln(3)#

#x=(ln(2)+ln(3))/(ln(3)-ln(2)#

But:
Addition of logs is the consequence of multiplication of the source numbers.

Subtraction of logs is the consequence of division of the source numbers.

#x=ln(6)/(ln(3/2))#

#x~~4.4190....#

#x~~4.42# to 2 decimal places.

Answer 2 · 2017-05-03T13:30:20

Solution to question 10

#x~~321.70# to 2 decimal places

#color(red)("You should be able to do questions 11 and 12 now")#

Note that #log_e(e)->ln(e)=1# as does #log_10(10)=1#

#10x[color(white)(.)ln(2)+ln(e)color(white)(.)]=19#

#x=19/(10(ln(2)+1))#

#x~~321.6979....#

#x~~321.70# to 2 decimal places

Answer 3 · 2017-05-03T14:21:43

#x=0.22512918#

10) #e^(10x )= 19/2 or e^(10x )= 9.5# taking log in both sides,

#10x*ln e =ln(9.5) or 10x =2.2512918 ; ln (e)=1:. x= 2.2512918/10=0.22512918# [Ans]