Verified answer

Given ln (2) = 0.69 and ln (5) = 1.61

(a) ln ( 1/10 ) = ln 10¯¹ = ( - 1 ) ln (10) = ( - 1 ) ln ( 5 * 2 ) = - 1 [ ln 2 + ln 5 ]

=> - 1 [ 0.69 + 1.61 ] = - 2.3 .............. Answer Answer

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(b) ln ( 5 /16 ) = ln 5 - ln 16 = ln 5 - ln ( 2 )^4 = ln 5 - 4 ln ( 2 )

=> 1.61 - 4 ( 0.69 ) b = - 1.15 ...................... Answer Answer

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(c) in [ 1 / (4√2) ] = ln (4√2)¯¹ = ( - 1 ) ln [ 4 * √2 ] = - 1 [ ln 2² + (1/2) ln 2 ]

=> - [ 2 ( 0.69 ) + (1/2) (0.69) ] = - 1.725 ................. Answer Answer

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Assuming that in is ln, we have:

ln2=0.69 and ln5=1.61

a)

ln(1/10)= ln(10/100) = ln10 - ln100 = ln(2*5) - ln (2*5*2*5)= ln2+ln5 - (ln2+ln5 + ln2 + ln5)=

= 0.69 + 1.61 - 2*(0.69+1.61)=2.3-4.6=-2.3

b)

ln(5/16)=ln5-ln16 = ln5-ln(2*2*2*2) =

=ln5 - (ln2+ln2+ln2+ln2)=

=1.61 - (0.69*4) =

= 1.61 - 2.76 =

= -1.15

c)

ln[1/4sqrt(2)] =

=ln10 - ln[10*4*(2)^1/2]=

=ln(2*5) - [ln(5*2*2*2*2)]/2=

=ln2+ln5 - (ln5+4*ln2)/2=

=2.3 -(1.61 + 2.76)/2

=-0.115

9^x=40 9 -----> log(9^x) = log(40 9) -----> x*log(9) = log(40 9) -----> x = log(40 9) / log(9) Use a calculator to determine that fee. you additionally can proceed and say: x = log(7^2) / log(3^2) = 2*log(7) / 2*log(3) = log(7) / log(3) however the respond is an identical. log 7+ log x=2 -----> log(7x) = 2 -----> because of the fact the backside isn't exact then it quite is 10 -----> 10^2 = 7x -----> x = 10^2 / 7 = a hundred/7 -----> x = 14.2857 i'm hoping this helps...