Solve for x 62^(x+3)=7^(2x+1)

$62^{x + 3} = 7^{2 x + 1}$

Step 1

Take the log of both sides of the equation.

$\ln (62^{x + 3}) = \ln (7^{2 x + 1})$

Step 2

Expand $\ln (62^{x + 3})$ by moving $x + 3$ outside the logarithm.

$(x + 3) \ln (62) = \ln (7^{2 x + 1})$

Step 3

Expand $\ln (7^{2 x + 1})$ by moving $2 x + 1$ outside the logarithm.

$(x + 3) \ln (62) = (2 x + 1) \ln (7)$

Step 4

Solve the equation for $x$ .

Simplify $(x + 3) \ln (62)$ .

Rewrite.

$0 + 0 + (x + 3) \ln (62) = (2 x + 1) \ln (7)$

Simplify by adding zeros.

$(x + 3) \ln (62) = (2 x + 1) \ln (7)$

Apply the distributive property.

$x \ln (62) + 3 \ln (62) = (2 x + 1) \ln (7)$

Simplify $(2 x + 1) \ln (7)$ .

Apply the distributive property.

$x \ln (62) + 3 \ln (62) = 2 x \ln (7) + 1 \ln (7)$

Multiply $\ln (7)$ by $1$ .

$x \ln (62) + 3 \ln (62) = 2 x \ln (7) + \ln (7)$

Subtract $2 x \ln (7)$ from both sides of the equation.

$x \ln (62) + 3 \ln (62) - 2 x \ln (7) = \ln (7)$

Subtract $3 \ln (62)$ from both sides of the equation.

$x \ln (62) - 2 x \ln (7) = \ln (7) - 3 \ln (62)$

Factor $x$ out of $x \ln (62) - 2 x \ln (7)$ .

Factor $x$ out of $x \ln (62)$ .

$x (\ln (62)) - 2 x \ln (7) = \ln (7) - 3 \ln (62)$

Factor $x$ out of $- 2 x \ln (7)$ .

$x (\ln (62)) + x (- 2 \ln (7)) = \ln (7) - 3 \ln (62)$

Factor $x$ out of $x (\ln (62)) + x (- 2 \ln (7))$ .

$x (\ln (62) - 2 \ln (7)) = \ln (7) - 3 \ln (62)$

Divide each term in $x (\ln (62) - 2 \ln (7)) = \ln (7) - 3 \ln (62)$ by $\ln (62) - 2 \ln (7)$ and simplify.

Divide each term in $x (\ln (62) - 2 \ln (7)) = \ln (7) - 3 \ln (62)$ by $\ln (62) - 2 \ln (7)$ .

$\frac{x (\ln (62) - 2 \ln (7))}{\ln (62) - 2 \ln (7)} = \frac{\ln (7)}{\ln (62) - 2 \ln (7)} + \frac{- 3 \ln (62)}{\ln (62) - 2 \ln (7)}$

Simplify the left side.

Cancel the common factor of $\ln (62) - 2 \ln (7)$ .

Cancel the common factor.

$\frac{x (\ln (62) - 2 \ln (7))}{\ln (62) - 2 \ln (7)} = \frac{\ln (7)}{\ln (62) - 2 \ln (7)} + \frac{- 3 \ln (62)}{\ln (62) - 2 \ln (7)}$

Divide $x$ by $1$ .

$x = \frac{\ln (7)}{\ln (62) - 2 \ln (7)} + \frac{- 3 \ln (62)}{\ln (62) - 2 \ln (7)}$

Simplify the right side.

Combine the numerators over the common denominator.

$x = \frac{\ln (7) - 3 \ln (62)}{\ln (62) - 2 \ln (7)}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (7) - 3 \ln (62)}{\ln (62) - 2 \ln (7)}$

Decimal Form:

$x = - 44.34708156 \dots$

Solve for x 62^(x+3)=7^(2x+1)

Related Questions

Support LCMGCF.com by disabling your adblocker.