How do you express ${log}_{3} 8$ $log_3 8$ in terms of common logarithms?

Question

3641 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-07T14:44:37

$x = \frac{log 8}{log 3}$ $x=log8/log3$

Let ${log}_{3} 8 = x$ $log_3 8=x$ , then we know that $3^{x} = 8$ $3^x=8$

Now taking common log (to base $10$ $10$ ) on both sides, we get

$x log 3 = log 8$ $xlog3=log8$

or $x = \frac{log 8}{log 3} = \frac{0.9031}{0.4771} = 1.8929$ $x=log8/log3=0.9031/0.4771=1.8929$

Note that ${log}_{a} b = \frac{log b}{log a}$ $log_ab=logb/loga$

How do you express log_3 8log38log_3 8 in terms of common logarithms?