How do you solve #2^x = 7#?

1 Answer
Johnson Z.
Mar 16, 2016

#x~~2.81#

Explanation:

#1#. Since the left and right sides of the equation do not have the same base, start by taking the log of both sides.

#2^x=7#

#log(2^x)=log(7)#

#2#. Use the log property, #log_color(purple)b(color(red)m^color(blue)n)=color(blue)n*log_color(purple)b(color(red)m)#, to simplify #log(2^x)#.

#xlog(2)=log(7)#

#3#. Solve for #x#.

#x=log(7)/log(2)#

#color(green)(|bar(ul(color(white)(a/a)x~~2.81color(white)(a/a)|)))#

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