Question

question
solve for x to the nearest 10th.
4.9 = 1.115^(3x) - 3
answer
x = |

Explanation:

Step1: Isolate the exponential term

Add 3 to both sides: $4.9 + 3 = 1.111^{3x}$ → $7.9 = 1.111^{3x}$

Step2: Take natural log of both sides

$\ln(7.9) = \ln(1.111^{3x})$ → $\ln(7.9) = 3x\ln(1.111)$

Step3: Solve for x

$x = \frac{\ln(7.9)}{3\ln(1.111)}$
Calculate values: $\ln(7.9)\approx2.066$, $\ln(1.111)\approx0.105$ → $x\approx\frac{2.066}{3\times0.105}\approx\frac{2.066}{0.315}\approx0.5$

Answer:

0.5