How do you solve #5^x + 4(5^(x+1)) = 63#?

1 Answer
Dec 16, 2015

#x=log_5(3)#

Explanation:

Given:
#color(white)("XXX")5^x+4(5^(x+1))=63#

Extract the common factor of #5^x# from both terms on the left side:
#color(white)("XXX")5^x(1+4(5^1))=63#
Simplify the numeric expression
#color(white)("XXX")5^x(21)=63#
Divide both sides by #21#
#color(white)("XXX")5^x=3#
Apply the equivalence: #log_b a =c hArr b^c=a#
#color(white)("XXX")x=log_5(3)#