Solve for k 4*10^k=60

$4 \cdot 10^{k} = 60$

Divide each term in $(4 \cdot 10^{k}) = 60$ by $4$ and simplify.

Divide each term in $(4 \cdot 10^{k}) = 60$ by $4$ .

$\frac{(4 \cdot 10^{k})}{4} = \frac{60}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 \cdot 10^{k}}{4} = \frac{60}{4}$

Divide $10^{k}$ by $1$ .

$10^{k} = \frac{60}{4}$

Simplify the right side.

Divide $60$ by $4$ .

$10^{k} = 15$

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

$\log (10^{k}) = \log (15)$

Expand the left side.

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

$k \log (10) = \log (15)$

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

$k \cdot 1 = \log (15)$

Multiply $k$ by $1$ .

$k = \log (15)$

The result can be shown in multiple forms.

Exact Form:

$k = \log (15)$

Decimal Form:

$k = 1.17609125 \dots$