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]