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MatroZZZ [7]
2 years ago
11

Use the change of Base formula to evaluate log5 92 . then convert. Log5 92 to a logarithm in base 3. Round to the nearest thousa

ndth.
Mathematics
2 answers:
Ad libitum [116K]2 years ago
8 0

Answer:

\log_5 92=2.809

\log_3 2.809=0.940            

Step-by-step explanation:

Given : Expression \log_5 92

To find : Use the Change of Base Formula to evaluate the expression also  convert the expression to a logarithm in base 3?

Solution :  

Applying the change of Base Formula,

i.e. \log_b x=\frac{log_a x}{\log_a b}

We get,

\log_5 92=\frac{\log 92}{\log 5}

\log_5 92=\frac{1.963}{0.698}

\log_5 92=2.809

So, The expression is \log_5 92=2.809

Now, converting the expression to a logarithm in base 3.

Taking log base 3 in 2.809,

\log_3 2.809=\frac{log 2.809}{\log 3}

\log_3 2.809=\frac{0.448}{0.477}

\log_3 2.809=0.940

Therefore, The solution is \log_3 2.809=0.940

vovikov84 [41]2 years ago
4 0
Change of base is
log_a(b)= \frac{log_c(b)}{log_c(a)}
change base to 3
log_5(92)= \frac{log_3(92)}{log_3(5)}
why would you want base 3? base 10 is on most calculators
anyway, the value would be 2.809555
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