Solving Equations with logarithims?

Then, 4/7=5^x/3^x=(5/3)^x, log 4/7=xlog (5/3), x=-1.0955
God bless you.

log(4)+x*log(3) = log(7) + x*log(5)
x*log(3) - x*log(5) = log(7) - log(4)

-.510825623*x = .559615788

x = - 1.095512368

2log base2x - log base2 (x+3) = 2 log base2 (x^2) - log base2 (x+3) = 2 log base 2 (x^2/(x+3) ) = 2 2^log base 2 (x^2/(x+3) ) = 2^2 x^2/(x+3) = 4 x^2 = 4 x + 12 x^2 -4 x -12 = 0 (x -6)(x+2) =0 x = 6 x = -2 discard as log base 2(x) isn't accessible

4 * 3^x = 7 * 5^x
3^x/(5^x) = 7/4
(3/5)^x = 7/4
log_0.6(0.6^x) = log_0.6(1.75)
x[log_0.6(0.6)] = log_0.6(1.75)
x = log_0.6(1.75) (-1.09551237)

You can put logs around both sides

log (4*3^x) = log (7*5^x)

Then use the rule:
log (ab) = log (a) + log (b)

log (4) + log (3^x) = log (7) + log (5^x)

Then use the rule:
log (a^b) = b log (a)

log (4) + x log (3) = log (7) + x log(5)

Now put common variables on both sides (one side with x's and other side without)
x log (3) - x log (5) = log (7) - log (4)

Now work out the log's. Either use log or ln (logaritmus naturalus)
I'll use both ways, first log: (which is standard log10)
0.477121x - 0.69897x = 0.84509 - 0.60205
-0.22184x = 0.24303

Now divide by -0.22184
x = -1.09555

The ln way: (which is log of e)
1.09861x - 1.60943x = 1.94591 - 1.38629
-0.510825x = 0.559615

Divide by -0.510825
x = -1.09555

Hope it helped ^^