How do you solve #2 times 3^x = 7 times 5^x#?

1 Answer
Tony B
Feb 28, 2016

I have taken you up to the final calculation!

Explanation:

Given: #" "2xx3^x=7xx5^x#

Collecting like terms

#2/7=5^x/3^x#

Taking logs of both sides ( have chosen to use Natural logs)

#color(brown)("Note that when taking logs, division of the source values becomes subtraction of the logs.")#
#color(brown)("Also "log(b^x) " can be written as "xlog(b))#

#ln(2)-ln(7)=ln(5^x) - ln(3^x)#

This may be can be written as:

#ln(2)-ln(7)=xln(5) -x ln(3)#

#ln(2)-ln(7)=x(ln(5)-ln(3))#

#x=(ln(2)-ln(7))/(ln(5)-ln(3) ) #

I will let you work this out!

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