How do you solve #5^x = 3^(x+2)#?

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Answer 1 · 2018-03-05T18:39:46

#x~~4.301color(white)(88)# 3.d.p.

#5^x=3^(x+2)#

Taking logarithms of both sides:

By the law of logarithms:

#lna^b=bln(a)#

#xln(5)=(x+2)ln(3)#

#xln(5)=xln(3)+2ln(3)#

Subtract #xln(3)# from both sides:

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

Factor #LHS#

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

Divide by #(ln(5)-ln(3))#

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

#x~~4.301color(white)(88)# 3.d.p.