Solve for x.

Question

53.)(e^2)^3x=[e^(2x)][e^(3x) answer is x=2/3    

54.)e^[3lnx-ln(x^3-2x+4)]=1 Answer is x=2  

55.)5^(2x)-2•5^(x+3)+5^(6)=0 Answer is x=3                                            

56.)lnx-ln(x+2)=1 answer is x=2e/1-e

Answer 1

53. 

(e²)^3x = (e^2x)(e^3x)

e^6x = e^5x

6x = 5x

x = 0

 

54. 

3lnx - ln(x³ - 2x + 4)

lnx³ - ln(x³ - 2x + 4)

ln[ x³ / (x³ - 2x + 4)

 

A law:

e^{ln a} = a

 

e raised the the expression above results in x³ / (x³ - 2x + 4)

 

55.

From where did you get this one?

 

56.

Argument for first "ln" is missing.