How do you calculate ${log}_{5} 310$ $log_5 310$ ?

Question

1514 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-09-01T13:19:30

$x = 3.564$ $x = 3.564$

${log}_{5} 310 = x$ $log_5 310 = x$

Change to index form.

$5^{x} = 310 \leftarrow$ $5^x = 310 larr$ variable is in the index log both sides.

${log 5}^{x} = log 310$ $log5^x = log310$

$x log 5 = log 310$ $xlog5 = log310$

$x = \frac{log 310}{log 5}$ $x = log310/log5$

Using a calculator or tables gives:

#x = 3.564

Using the "Change of base law" gives the same result.

${log}_{a} b = \frac{log b}{log a}$ $log_a b = (logb)/(loga)$

How do you calculate log5310log_5 310?