Use logarithmic properties and the fact that ln(2) ≈ 0.69 and ln(3) ≈ 1.10 to approximate the value of each of the
following logarithmic expressions. Do not use a calculator.
ln(8/3)

Hi, we need to use the log properties taking into account that Ln(2) is aprox. 0.69 and Ln(3) is aprox. 1.10. I think you can understand better as we solve it, so here it goes.

[tex]Ln(\frac{8}{3} )=Ln(8)-Ln(3)[/tex]

Since:

[tex]8=2^{3}[/tex]

[tex]Ln(2^{3} )-Ln(3)[/tex]

Then

[tex]3Ln(2)-Ln(3)[/tex]

Now, we have everything where we want it, in terms of Ln(2) and Ln(3), now it is easy to solve.

[tex]3(0.69)-1.10[/tex]

[tex]2.07-1.10=0.97[/tex]

Best of luck.

Use logarithmic properties and the fact that ln(2) ≈ 0.69 and ln(3) ≈ 1.10 to approximate the value of each of the following logarithmic expressions. Do not use a calculator. ln(8/3)

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Use logarithmic properties and the fact that ln(2) ≈ 0.69 and ln(3) ≈ 1.10 to approximate the value of each of the
following logarithmic expressions. Do not use a calculator.
ln(8/3)