Question

Danielle is trying to solve the equation 25^x+3=176 Explain in detail how Danielle should solve this problem. Then solve it step by step showing all your work and tell Danielle what the answer should be.

Answer 1

Given:

Equation is:

`\begin{gathered} 25^x+3=176 \\ \end{gathered}`

Find-:

Solve the equation

Explanation-:

Simplify the equation then,

`\begin{gathered} 25^x+3=176 \\ \\ 25^x=176-3 \\ \\ 25^x=173 \\ \\ 5^(2x)=173 \end{gathered}`

Taking ln both sides then,

`\ln5^(2x)=\ln173`

Use logarithmic property

`\ln a^b=b\ln a`

Then the value is:

`\begin{gathered} \ln5^(2x)=\ln173 \\ \\ 2x\ln5=\ln173 \\ \\ 2x=(\ln173)/(\ln5) \\ \\ x=(\ln173)/(2\ln5) \end{gathered}`

The value of "x" is:

`\begin{gathered} x=(\ln173)/(2\ln5) \\ \\ x=(5.1533)/(2*1.6094) \\ \\ x=(5.1533)/(3.2189) \\ \\ x=1.601 \end{gathered}`

So, the value of "x" is 1.601