Question

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

Answer 1

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 $\log_3 2.809=0.940$

Answer 2

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