mathpi.netIn this class, we will answer: What is the Logarithm of 6 to the base 8. We will then have a step-by-step solution on how to find the value of \(\log_{8}{(6)}.\)
Answer
Logarithm of 6 to the base 8 is 0.861654.
\(\log_{8}(6) = 0.861654\)
Inputs
Step-by-step Solution to Find Logarithm of 6 to the Base 8
Given
\(a = 6\)
\(b = 8\)
Find
We have to find the value of \(\log_{8}(6)\).
Computing Logarithm...
Step 1
Express a(=6) in terms of power of b(=8).
\(6 = 8^{0.861654}\)
Step 2
Apply natural logarithm to both sides.
\(\log_{e}{6} = \log_{e}{8^{0.861654}}\)
We know that \(\log_{e}{m^n} = n \times \log_{e}{m} \). Apply this formula to \(\log_{e}{8^{0.861654}}\), the value on right side in the above equation.
\(\log_{e}{6} = 0.861654\times \log_{e}{8}\)
Step 3
Divide both sides by \(\log_{e}{8}\).
\(\frac{\log_e{6}}{\log_e{8}} = \frac{0.861654\times \log_e{8}}{\log_e{8}}\)
Cancel common term from numerator and denominator on the right side.
\(\frac{\log_e{6}}{\log_e{8}} = 0.861654\)
We know that \(\frac{\log_e{m}}{\log_e{n}} = \log_n{m} \). Apply this formula to the value on left side in the above equation.
\(\log_{8}{6} = 0.861654\)
Result
\(\log_{8}(6) = 0.861654\)
Logarithms of Nearby Numbers
| \(\log_{8}{a} = ?\) | Step-by-step Solution |
|---|---|
| \(\log_{8}{1} = 0\) | Log of 1 to base 8 |
| \(\log_{8}{2} = 0.333333\) | Log of 2 to base 8 |
| \(\log_{8}{3} = 0.528321\) | Log of 3 to base 8 |
| \(\log_{8}{4} = 0.666667\) | Log of 4 to base 8 |
| \(\log_{8}{5} = 0.773976\) | Log of 5 to base 8 |
| \(\log_{8}{6} = 0.861654\) | Log of 6 to base 8 |
| \(\log_{8}{7} = 0.935785\) | Log of 7 to base 8 |
| \(\log_{8}{8} = 1\) | Log of 8 to base 8 |
| \(\log_{8}{9} = 1.056642\) | Log of 9 to base 8 |
| \(\log_{8}{10} = 1.107309\) | Log of 10 to base 8 |
| \(\log_{8}{11} = 1.153144\) | Log of 11 to base 8 |