Logarithmic Equations: Difficult Problems with Solutions

Problem 1
Find the root of the equation: [tex]log_3(3^{2x}-3^x+1)=x[/tex]
Problem 2
Determine the value of x, if
Problem 3
Problem 4
Solve the logarithmic equation [tex]log_7(x^3-3x^2+3x-1)=6[/tex]
Problem 5
Find the solution to the equation
Problem 6
Solve the equation: [tex]\frac{lg8x}{lg|7x+3|}=1[/tex]
Problem 7
Solve the equation [tex]log_5x-log_{25}x+log_{\sqrt{5}}x=-5[/tex]
Problem 8
Solve the equation [tex]log_3(28-3^x)=2^{log_2(3-x)}[/tex]
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