How do you solve $- 4 \cdot 3^{5 x} - 4 = - 30$ $-4*3^(5x)-4=-30$ ?

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Answer 1 · 2018-04-20T08:00:12

$x = \frac{ln (\frac{13}{2})}{5 ln (3)} \approx 0.3407575530$ $color(blue)(x=ln(13/2)/(5ln(3))~~0.3407575530)$

$- 4 \cdot 3^{5 x} - 4 = - 30$ $-4*3^(5x)-4=-30$

Add 4 to both sides:

$- 4 \cdot 3^{5 x} = - 26$ $-4*3^(5x)=-26$

Multiply by $- 1$ $-1$ :

$4 \cdot 3^{5 x} = 26$ $4*3^(5x)=26$

Divide by 4:

$3^{5 x} = \frac{13}{2}$ $3^(5x)=13/2$

Taking natural logarithms of both sides:

$5 x ln (3) = ln (\frac{13}{2})$ $5xln(3)=ln(13/2)$

Divide by $5 ln (3)$ $5ln(3)$ :

$x = \frac{ln (\frac{13}{2})}{5 ln (3)} \approx 0.3407575530$ $x=ln(13/2)/(5ln(3))~~0.3407575530$

How do you solve −4⋅35x−4=−30-4*3^(5x)-4=-30?