how to solve logarithm equation

i want to solve an logarithm equation and find the value of x

log10(x^4)-log10(x^3) == log10(5*x) -log10(2*x)

[Davide Masiello]

I believe that reduces to

and therefore there's no real solution to it

log10(4/3) == log10(5/2)

ans = logical
   0

[MANANJAYA NAYAK]

yes its there but in code how to solve and find the x value

[Ghazwan]

syms a b c x
eqn = a*x^2 + b*x + c == 0
S = solve(eqn)

[David Hill]

Use fzero to solve a non-linear equation numerically. fzero

Answer 1

[David Hill]

f=@(x)log10(x.^4)-log10(x.^3)-log10(5*x) +log10(2*x);
fzero(f,2)

ans = 2.5000

x=.1:.1:10;
plot(x,f(x));

Answer 2

[David Hill]

if you plot, it never crosses zero.

f=@(x)log10(4*x)-log10(3*x) -log10(5*x) +log10(2*x)

f = function_handle with value:
    @(x)log10(4*x)-log10(3*x)-log10(5*x)+log10(2*x)

fzero(f,1)

Exiting fzero: aborting search for an interval containing a sign change
    because NaN or Inf function value encountered during search.
(Function value at -4.06772e+307 is -Inf.)
Check function or try again with a different starting value.

ans = NaN

Answer 3

[Torsten]

log10(4*x)-log10(3*x) = log10((4*x)/(3*x)) = log10(4/3)
log10(5*x)-log10(2*x) = log10((5*x)/(2*x)) = log10(5/2)

So you try to "solve"

log10(4/3) = log10(5/2)

You can imagine that this makes no sense.