Solve for x 10^(x-1)=e

$10^{x - 1} = e$

Step 1

Take the base $10$ logarithm of both sides of the equation to remove the variable from the exponent.

$\log (10^{x - 1}) = \log (e)$

Step 2

Expand the left side.

Expand $\log (10^{x - 1})$ by moving $x - 1$ outside the logarithm.

$(x - 1) \log (10) = \log (e)$

Logarithm base $10$ of $10$ is $1$ .

$(x - 1) \cdot 1 = \log (e)$

Multiply $x - 1$ by $1$ .

$x - 1 = \log (e)$

Step 3

Add $1$ to both sides of the equation.

$x = \log (e) + 1$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \log (e) + 1$

Decimal Form:

$x = 1.43429448 \dots$