danika44
Answered

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Write the expression 2 in3 + in8 as a single natural logarithm.

Sagot :

elcharly64

Answer:

[tex]2\ln 3+\ln 8=\ln 72[/tex]

Step-by-step explanation:

Logarithms

Some properties of the logarithms are:

[tex]\ln xy = \ln x+\ln y[/tex]

[tex]\ln x^n=n\ln x[/tex]

We have:

[tex]2\ln 3+\ln 8[/tex]

Applying the exponent property:

[tex]2\ln 3+\ln 8=\ln 3^2+\ln 8=\ln 9+\ln 8[/tex]

Applying the product property:

[tex]2\ln 3+\ln 8=\ln (9*8)=\ln 72[/tex]

[tex]\boxed{2\ln 3+\ln 8=\ln 72}[/tex]

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