How do you solve #(1.5)^(3x)=7.5#?

1 Answer
Johnson Z.
Mar 17, 2016

#x~~1.66#

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.

#1.5^(3x)=7.5#

#log(1.5^(3x))=log(7.5)#

#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 the left side of the equation.

#(3x)log1.5=log7.5#

#3#. Solve for #x#.

#3x=log7.5/log1.5#

#x=log7.5/(3log1.5)#

#color(green)(|bar(ul(color(white)(a/a)x~~1.66color(white)(a/a)|)))#

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