Schoolcrop

(Q50).Solve the equation 3^x = 5^x-2

x log₁₀ = (x-2) log₁₀

x log₁₀ = xlog₁₀ - 2log₁₀

xlog₁₀ - 2log₁₀ = x log₁₀

xlog₁₀ - x log₁₀ = 2 log₁₀

x(log₁₀ - log₁₀) = 2 log₁₀

So,

x =

log₁₀

log - log

So it is

x =

log₁₀

log - log