Answered

At Westonci.ca, we connect you with experts who provide detailed answers to your most pressing questions. Start exploring now! Experience the ease of finding reliable answers to your questions from a vast community of knowledgeable experts. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

Consider [tex]\(8^{x-4} = 8^{10}\)[/tex].

Because the bases are equal, the exponents must also be equal.

Sagot :

GinnyAnswer
Certainly! Let's solve the equation step-by-step.

Given equation:
[tex]\[ 8^{x-4} = 8^{10} \][/tex]

### Step 1: Understanding the Equation
We have an equation in which both sides have the same base, which is 8.

### Step 2: Equating the Exponents
Because the bases are equal, in order for the equation to hold true, the exponents themselves must be equal. Therefore, we can set the exponents equal to each other:
[tex]\[ x - 4 = 10 \][/tex]

### Step 3: Solving for [tex]\( x \)[/tex]
Now, we need to isolate [tex]\( x \)[/tex] on one side of the equation. To do this, we add 4 to both sides of the equation:
[tex]\[ x - 4 + 4 = 10 + 4 \][/tex]
[tex]\[ x = 14 \][/tex]

### Conclusion
Thus, the value of [tex]\( x \)[/tex] that satisfies the given equation is:
[tex]\[ x = 14 \][/tex]

So, the solution to the equation [tex]\( 8^{x-4} = 8^{10} \)[/tex] is [tex]\( x = 14 \)[/tex].
We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.