Logarithms help please

How do I find the value of x on these:

a) (1.5)^2x=10

b) 5log5(3x)=6

c) log3x+log3(2x)=3

I'm absolutely confused; my classwork didn't have questions like this but my homework does.
How do I work these out?

Thank you greatly!

a) 2xlog1.5=log10=1
2x=1/log1.5=5.6788
x=2.84
--------------------------------------…
b) log5(3x)=6/5=1.2
3x=5^1.2=6.8986
x=2.3
--------------------------------------…
c) log3 2x^2=3
2x^2=3^3=27
x^2=27/2
x=+3.674
God bless you.

a)
(1.5)^2x = 10
2.25x = 10
x = 10/2.25
If you meant (1.5)^(2x) = 10, then
(1.5)^(2x) = 10
ln(1.5^(2x)) = ln10
2xln1.5 = ln10
2x = ln10/ln1.5
x = ln10/(2ln1.5)

b) 5log(base 5)(3x) = 6
log(base 5)(3x) = 6/5
5^(log(base 5)(3x)) = 5^(6/5)
3x = 5^(6/5)
x = 5^(6/5)/3

c) log(base 3)x + log(base 3)(2x) = 3
log(base 3)(x * 2x) = 3
log(base 3)(2x^2) = 3
3^3 = 2x^2
27 = 2x^2
x^2 = 27/2
x = √(27/2) or x = -√(27/2)