Need help with some logarithmic equations?

Can someone lay these problems out in their steps, I have no idea how to do them

solve 5^(3x)=25^(2x+1) Hint 5^2=25

solve ln x^2-ln 2 = ln (3x-4)

Thank you…

Top 1 Answers

A few days ago

Anonymous

Favorite Answer

Question 1:

5^(3x)=25^(2x+1)

ln(5^(3x))=ln(25^(2x+1))

3x*ln5=(2x+1)*ln25

3x*ln5=2x*ln25+ln25

3x*ln5-2x*ln25=ln25

x*(3*ln5-2*ln25)=ln25

x=ln25/(3*ln5-2*ln25)

x=-2

Question 2:

lnx^2-ln2=ln(3x-4)

ln(x^2/2)=ln(3x-4)

x^2/2=3x-4

x^2/2-3x+4=0

then use the quadratic equation

x=(3+((-3)^2-4*1/2*4)^.5)/ (2*1/2)

x=(3-((-3)^2-4*1/2*4)^.5)/ (2*1/2)

x=4 or 2

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