Question

Hello. Can you please assist with the following question? 3(5)2x + 10 = 9

Answer 1

No solution

Step-by-step explanation

We want to find the solution to the equation given:

`3(5)^(2x)+10=9`

First, subtract 10 from both sides of the equation:

`\begin{gathered} 3(5)^(2x)+10-10=9-10 \\ 3(5)^(2x)=-1 \end{gathered}`

Next, divide both sides by 3:

`\begin{gathered} (3)/(3)(5)^(2x)=(-1)/(3) \\ 5^(2x)=(-1)/(3) \end{gathered}`

Now, convert from an exponential equation to a logarithmic equation as follows:

`\begin{gathered} x^a=b \\ \Rightarrow\log _xb=a \end{gathered}`

Therefore, we have that:

`\log _5(-(1)/(3))=2x`

Since the logarithm of a negative number cannot be mathematically found, we can conclude that there is no solution for x which satisfies the given equation.