Answer :
Let's solve the equation [tex]\(6 \times 10^x = 60000\)[/tex] step-by-step using the like-bases property of exponents.
1. Isolate [tex]\(10^x\)[/tex]:
Start by dividing both sides of the equation by 6 to isolate [tex]\(10^x\)[/tex].
[tex]\[
10^x = \frac{60000}{6}
\][/tex]
2. Perform the division:
Simplifying the division gives:
[tex]\[
10^x = 10000
\][/tex]
3. Use the property of exponents:
We know [tex]\(10^x = 10000\)[/tex]. Recognizing that [tex]\(10000\)[/tex] is a power of 10, we can express it as [tex]\(10^4\)[/tex].
4. Solve for [tex]\(x\)[/tex]:
Since the bases are the same, we can equate the exponents:
[tex]\[
x = 4
\][/tex]
Therefore, the solution to the equation [tex]\(6 \times 10^x = 60000\)[/tex] is [tex]\(x = 4\)[/tex].
1. Isolate [tex]\(10^x\)[/tex]:
Start by dividing both sides of the equation by 6 to isolate [tex]\(10^x\)[/tex].
[tex]\[
10^x = \frac{60000}{6}
\][/tex]
2. Perform the division:
Simplifying the division gives:
[tex]\[
10^x = 10000
\][/tex]
3. Use the property of exponents:
We know [tex]\(10^x = 10000\)[/tex]. Recognizing that [tex]\(10000\)[/tex] is a power of 10, we can express it as [tex]\(10^4\)[/tex].
4. Solve for [tex]\(x\)[/tex]:
Since the bases are the same, we can equate the exponents:
[tex]\[
x = 4
\][/tex]
Therefore, the solution to the equation [tex]\(6 \times 10^x = 60000\)[/tex] is [tex]\(x = 4\)[/tex].
