Question

5lg 20 : 20lg5+1 =?​

Answer 1

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$\frac{5^{log20} }{20^{log5+1} } = \frac{5^{log(2^{.} 10) } }{20^{.} 20^{log5} } =$

$\frac{5^{log2 + log10} }{20^{.}(2^{.}10)^{(log5)} }= \frac{5^{log^{2+1}} }{20^{.}2^{log5} ^{.}10^{log5}}=$

$\frac{5}{20} ^{.}\frac{5^{log2}}{2^{log} ^{.}5} = \frac{1}{20} ^. \frac{5^{log5} ^{.} 5^{log2}}{5^{log5} ^. 2^{log5}} =$

$\frac{1}{20} ^. \frac{5^{log5+ log2}}{10^{log5}} = \frac{1}{20} ^. \frac{5^{log(5^. 2)}}{10^{log5}} =$

$\frac{1}{20} ^. \frac{5^{1} }{5} = \frac{1}{20}$

Answer 2

To solve this equation, you can use the properties of logarithms.

First, let's simplify each side of the equation step by step:

1. 5lg(20) = lg(20^5) because the logarithm property allows you to bring the exponent inside the logarithm.
2. 5lg(20) = lg(320000) because 20^5 is equal to 320000.

Now, let's simplify the right side of the equation:

1. 20lg(5) + 1 = lg(5^20) + 1 because the logarithm property allows you to bring the exponent inside the logarithm.
2. 20lg(5) + 1 = lg(95367431640625) + 1 because 5^20 is equal to 95367431640625.

So, the equation becomes:

lg(320000) = lg(95367431640625) + 1

Now, since the logarithms on both sides of the equation have the same base (base 10), the quantities inside the logarithms must be equal:

320000 = 95367431640625

However, it's clear that these two numbers are not equal, so the equation:

5lg(20) = 20lg(5) + 1

does not have a solution with real numbers.