Solve for r 2*8^(5r)=28

$2 \cdot 8^{5 r} = 28$

Simplify.

Rewrite $8$ as $2^{3}$ .

$2 \cdot {(2^{3})}^{5 r} = 28$

Multiply the exponents in ${(2^{3})}^{5 r}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$2 \cdot 2^{3 (5 r)} = 28$

Multiply $5$ by $3$ .

$2 \cdot 2^{15 r} = 28$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2^{1 + 15 r} = 28$

Divide each term in $2^{1 + 15 r} = 28$ by $2$ and simplify.

Divide each term in $2^{1 + 15 r} = 28$ by $2$ .

$\frac{2^{1 + 15 r}}{2} = \frac{28}{2}$

Simplify the left side.

Cancel the common factor of $2^{1 + 15 r}$ and $2$ .

Factor $2$ out of $2^{1 + 15 r}$ .

$\frac{2 \cdot 2^{15 r}}{2} = \frac{28}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$\frac{2 \cdot 2^{15 r}}{2 (1)} = \frac{28}{2}$

Cancel the common factor.

$\frac{2 \cdot 2^{15 r}}{2 \cdot 1} = \frac{28}{2}$

Rewrite the expression.

$\frac{2^{15 r}}{1} = \frac{28}{2}$

Divide $2^{15 r}$ by $1$ .

$2^{15 r} = \frac{28}{2}$

Simplify the right side.

Divide $28$ by $2$ .

$2^{15 r} = 14$

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

$\ln (2^{15 r}) = \ln (14)$

Expand $\ln (2^{15 r})$ by moving $15 r$ outside the logarithm.

$15 r \ln (2) = \ln (14)$

Divide each term in $15 r \ln (2) = \ln (14)$ by $15 \ln (2)$ and simplify.

Divide each term in $15 r \ln (2) = \ln (14)$ by $15 \ln (2)$ .

$\frac{15 r \ln (2)}{15 \ln (2)} = \frac{\ln (14)}{15 \ln (2)}$

Simplify the left side.

Cancel the common factor of $15$ .

Cancel the common factor.

$\frac{15 r \ln (2)}{15 \ln (2)} = \frac{\ln (14)}{15 \ln (2)}$

Rewrite the expression.

$\frac{r \ln (2)}{\ln (2)} = \frac{\ln (14)}{15 \ln (2)}$

Cancel the common factor of $\ln (2)$ .

Cancel the common factor.

$\frac{r \ln (2)}{\ln (2)} = \frac{\ln (14)}{15 \ln (2)}$

Divide $r$ by $1$ .

$r = \frac{\ln (14)}{15 \ln (2)}$

The result can be shown in multiple forms.

Exact Form:

$r = \frac{\ln (14)}{15 \ln (2)}$

Decimal Form:

$r = 0.25382366 \dots$

Solve for r 2*8^(5r)=28

Related Questions

Support LCMGCF.com by disabling your adblocker.