ln (5x-2)=12 approximate the solution to four decimal places

Question

nowhereman · Answer

Here you apply three functions to x [5*•, •-2, ln •] and want a point x with a certain function value. Luckily all these functions are injective (one-to-one, monomorphisms). So you can simply apply the inverse functions in inverse order to 12, so first the inverse of ln, which is exp, then the inverse function of •-2 and then the inverse function of 5*•.

anonymous · Answer

how would u write that

anonymous · Answer

$$ln(5x-2) = 12$$
$$\implies 5x-2 = e^{12}$$
And continue to solve for x.

anonymous · Answer

Remember that
$$e^{ln\ a}=a$$
So were just raising e to the power of each side of the equation to remove the natural log function.

anonymous · Answer

would the answer be -1.3523

anonymous · Answer

No. It's definitely not a negative number.

anonymous · Answer

could u show me how to get the answer

anonymous · Answer

How would you solve 5x - 2 = 162754