Solve for x: (ax)^loga=(bx)^logb
(ax)^log(a) = (bx)^log(b)
log(a) * log(ax) = log(b) * log(bx)
log(a) / log(b) = log(bx) / log(ax)
log(a) / log(b) = [log(b) + log(x)] / [log(a) + log(x)]
[log(a) / log(b)] * [log(a) + log(x)] = log(b) + log(x)
[log^2(a) / log(b)] + [log(a) * log(x) / log(b)] = log(b) + log(x)
[log^2(a) / log(b)] - log(b) = log(x) - [log(a) * log(x) / log(b)]
[log^2(a) / log(b)] - log(b) = log(x) [1 - log(a) / log(b)]
{[log^2(a) / log(b)] - log(b)} / [1 - log(a) / log(b)] = log(x)
x = 10^{ {[log^2(a) / log(b)] - log(b)} / [1 - log(a) / log(b)] }
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(ax)^log(a) = (bx)^log(b)
log(a) * log(ax) = log(b) * log(bx)
log(a) / log(b) = log(bx) / log(ax)
log(a) / log(b) = [log(b) + log(x)] / [log(a) + log(x)]
[log(a) / log(b)] * [log(a) + log(x)] = log(b) + log(x)
[log^2(a) / log(b)] + [log(a) * log(x) / log(b)] = log(b) + log(x)
[log^2(a) / log(b)] - log(b) = log(x) - [log(a) * log(x) / log(b)]
[log^2(a) / log(b)] - log(b) = log(x) [1 - log(a) / log(b)]
{[log^2(a) / log(b)] - log(b)} / [1 - log(a) / log(b)] = log(x)
x = 10^{ {[log^2(a) / log(b)] - log(b)} / [1 - log(a) / log(b)] }