Question

Solve the equation (2.05)^x = 18 for x, Find x

Answer 1

Step 1:

To solve the equation:

`(\text{ 2. 05 \rparen}^x=\text{ 18}`

The details of the solution are as follows:

Taking the logarithm of both sides, we have that:

`\begin{gathered} log\text{ \lparen2.05\rparen}^{x\text{ }}=\text{ log 18} \\ This\text{ means that:} \\ \text{x log \lparen2.05\rparen = log 18} \\ Divide\text{ both sides by log 2.05, we have that:} \end{gathered}`
`x\text{ =}\frac{log\text{ 18}}{log\text{ 2.05}}\text{ \lparen OPTION C \rparen}`

CONCLUSION:

The final answer is:

`x\text{ =}\frac{log\text{ 18}}{log\text{ 2.05}}\text{ \lparen OPTION C \rparen}`