Express 125 = 5x as a logarithmic equation.

Mathematics

2 answers:

Mrrafil [7]3 years ago

4 0

Log 5 to the power of 125 equals X

Step2247 [10]3 years ago

3 0

Answer: Hello mate!

I guess here says:

125 = 5^x

and we want to express this equation in logaritmic form:

using the relation:

ln(a^b) = b*ln(a)

we can solve the previous equation for x as:

125 = 5^x

apply ln to both sides:

ln(125) = ln(5^x)

ln(125) = xln(5)

x = ln(125)/ln(5)

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45% of the population of a city are men

leonid [27]

Answer:

$\boxed{\textsf{ The number of children is \textbf{24150}.}}$

Step-by-step explanation:

Given that the 45% of the population of a city are men and 15% are children . The number of women is 64,400 . And we need to find the number of children . Here ,

$\sf\implies Percentage_{(men)}= 45/% .\\\\\sf\implies Percentage_{(children)}= 15\% .$

So the percentage of women will be equal to [ 100 - ( 45 -15) ]% = [ 100 - 60 ]% = 40% .

So let us take the total number of people be x . So ,

$\purple{\bigstar}\underline{\underline{\boldsymbol{ According\ to \ Question :- }}}$

$\sf\implies 40\% \ of \ x \ = \ 64,400 \\\\\sf\implies \dfrac{40x}{100}= 64,400 \\\\\sf\implies x =\dfrac{64,400\times 100}{40}\\\\\sf\implies \boxed{\pink{\sf x = 161,000 }}$

$\rule{200}2$

The percentage of children = 15% :-

$\sf\implies Number_{(children)}= 15\% \ of 161,000\\\\\sf\implies Number_{(children)}= \dfrac{15}{100}\times 161,000 \\\\\sf\implies \boxed{\pink{\frak {Number_{(children)}= 24150 }}}$