2. The log3 20 can be written as
(1) 2log, 2+ log, 5
(3) log, 15+log, 5
(2) 2 log, 10
(4) 2log, 4+3log, 4

Question

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Respuesta :

berno berno · Answer 1 · 2020-06-02T09:32:10+02:00

Answer:

[tex]2\log _32+\log _35[/tex]

Step-by-step explanation:

Given: [tex]\log _3 20[/tex]

To find: the correct option

Solution:

The logarithm function is the inverse function to exponentiation function.

Domain of a logarithmic function = set of real numbers greater than zero Range of a logarithmic function = set of real numbers

[tex]\log _3 20=\log _3(2^2\times 5)[/tex]

As [tex]\log _a(xy)=\log _ax+\log _ay[/tex],

[tex]\log _3 20=\log _32^2+\log _35[/tex]

As [tex]\log _ax^y=y\log _ax[/tex] ,

[tex]\log _3 20=\log _32^2+\log _35\\=2\log _32+\log _35[/tex]

MrRoyal MrRoyal · Answer 2 · 2021-11-18T10:21:12+01:00

Expressions can be converted to and from logarithmic forms

[tex]\mathbf{log_320 }[/tex] can be rewritten as: [tex]\mathbf {log_3(4) +log_3(5)}[/tex]

The expression is given as:

[tex]\mathbf{log_320}[/tex]

Express 20 as 4 * 5

[tex]\mathbf{log_320 = log_3(4 \times 5)}[/tex]

Apply law of logarithm: Split the expression

[tex]\mathbf{log_320 = log_3(4) +log_3(5)}[/tex]

The above equation means that:

[tex]\mathbf{log_320 }[/tex] can be rewritten as: [tex]\mathbf {log_3(4) +log_3(5)}[/tex]

Hence, the equivalent expression of [tex]\mathbf{log_320 }[/tex] is [tex]\mathbf {log_3(4) +log_3(5)}[/tex]