How do you solve #5^x = 10#?

1 Answer
Alan P.
Feb 24, 2016

#x=log_5 10 ~~1.430677#

Explanation:

Make use of the standard relationship
#color(white)("XXX")log_b a = c <=> b^c = a#
or (reversed)
#color(white)("XXX")b^c=a <=> log_b a#

So
#color(white)("XXX")5^x= 10 <=> log_5 10 = x#

#log_5 10# can be evaluated using a calculator as #~~1.430677#

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