Question

Please help me solve ( solving exponential and logarithmic equations)

Answer 1

Step 1:

Write the equation

`(2)/(5)\text{ }\cdot\text{ 4}^(5x)\text{ - 8 = 4}`

Step 2:

Multiply each term by 5 to cancel out the denominator.

Step 3:

Divide through by 2

Step 4:

Take the natural logarithm of both sides

`\begin{gathered} 4^(5x)\text{ = 30} \\ ln(4)^(5x)\text{ = ln\lparen30\rparen} \\ \text{5x ln\lparen4\rparen = ln\lparen30\rparen} \\ \text{5x = }(ln(30))/(ln(4)) \\ \text{5x = 2.453445298} \\ \text{ x = }(2.453445298)/(5) \\ x=0.49068 \end{gathered}`

Final answer

x = 0.49068