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How do you calculate #Log_10 root3(10 )#?

Answer 1

Liam Brennan

For this problem, you will use the following log properties: #log_aa = 1# and #root(n)(m)= m^(1/n)#

#log_10(10^(1/3))#

Use the log property #loga^n= nloga#

#= 1/3log_10(10)#

#= 1/3#

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Answer 2

Serenity Jones

To calculate ( \log_{\sqrt[3]{10}}{10} ), you can use the change of base formula for logarithms, which states that ( \log_{b}{x} = \frac{\log_{c}{x}}{\log_{c}{b}} ) for any positive real numbers ( x ), ( b ), and ( c ) where ( b \neq 1 ) and ( c \neq 1 ). So, for this calculation, you can choose any base you prefer, such as base 10 or base ( e ). Here, we'll use base 10:

( \log_{\sqrt[3]{10}}{10} = \frac{\log_{10}{10}}{\log_{10}{\sqrt[3]{10}}} )

Since ( \log_{10}{10} = 1 ), the calculation simplifies to:

( \frac{1}{\log_{10}{\sqrt[3]{10}}} )

Now, we need to find ( \log_{10}{\sqrt[3]{10}} ). Since ( \sqrt[3]{10} ) is the same as ( 10^{1/3} ), we have:

( \log_{10}{\sqrt[3]{10}} = \log_{10}{10^{1/3}} = \frac{1}{3} )

Therefore, ( \log_{\sqrt[3]{10}}{10} = \frac{1}{\frac{1}{3}} = 3 ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.