Question

use common logarithms or natural logarithms an\
\\(\log_{26}390\\)\
\\(\bigcirc\\) 0.5461\
\\(\bigcirc\\) 1.8312\
\\(\bigcirc\\) 4.0060\
\\(\bigcirc\\) 1.1761

Explanation:

Step1: Apply Change of Base Formula

The change of base formula for logarithms is $\log_{b}a = \frac{\log a}{\log b}$ (or $\frac{\ln a}{\ln b}$). For $\log_{26}390$, we can use common logarithms (base 10) or natural logarithms. Let's use common logarithms: $\log_{26}390=\frac{\log 390}{\log 26}$.

Step2: Calculate Logarithms

First, find $\log 390$. Using a calculator, $\log 390\approx2.59106$. Then, find $\log 26$. Using a calculator, $\log 26\approx1.41497$.

Step3: Divide the Logarithms

Now, divide these two values: $\frac{2.59106}{1.41497}\approx1.8312$.

Answer:

1.8312 (corresponding to the option "1.8312")