How do you calculate ${log}_{24} 356$ $log _24 356$ ?

Question

1869 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-06-22T09:14:50

1.849

Use the change of base law:

${log}_{24} 356 = \frac{log 356}{log 24}$ $log_24 356 = (log 356)/(log24)$

This is calculated on a calculator to give: 1.849

The same result can be obtained from using index form first:

Let ${log}_{24} 356 = x$ $log_24 356 = x$

$24^{x} = 356$ $24^x = 356$

${log 24}^{x} = log 356$ $log24^x = log356$

$x log 24 = 356$ $xlog24 = 356$

$x = \frac{log 356}{log 24} = 1.849$ $x = (log356)/(log24) = 1.849$

How do you calculate log24356log _24 356?