Answer :
Sure! Let's solve the equation [tex]\( 6 \times 10^n = 60000 \)[/tex] step-by-step using the like bases property.
1. Start by isolating the term with the variable [tex]\( n \)[/tex]:
The given equation is:
[tex]\[
6 \times 10^n = 60000
\][/tex]
To isolate [tex]\( 10^n \)[/tex], divide both sides of the equation by 6:
[tex]\[
10^n = \frac{60000}{6}
\][/tex]
2. Perform the division:
[tex]\[
10^n = 10000
\][/tex]
3. Express 10000 as a power of 10:
Notice that 10000 can be rewritten as [tex]\( 10^4 \)[/tex], because:
[tex]\[
10^4 = 10 \times 10 \times 10 \times 10 = 10000
\][/tex]
4. Use the property of exponents:
Since both sides of the equation have the same base (10), we can equate the exponents:
[tex]\[
n = 4
\][/tex]
So, the solution to the equation [tex]\( 6 \times 10^n = 60000 \)[/tex] is [tex]\( n = 4 \)[/tex].
1. Start by isolating the term with the variable [tex]\( n \)[/tex]:
The given equation is:
[tex]\[
6 \times 10^n = 60000
\][/tex]
To isolate [tex]\( 10^n \)[/tex], divide both sides of the equation by 6:
[tex]\[
10^n = \frac{60000}{6}
\][/tex]
2. Perform the division:
[tex]\[
10^n = 10000
\][/tex]
3. Express 10000 as a power of 10:
Notice that 10000 can be rewritten as [tex]\( 10^4 \)[/tex], because:
[tex]\[
10^4 = 10 \times 10 \times 10 \times 10 = 10000
\][/tex]
4. Use the property of exponents:
Since both sides of the equation have the same base (10), we can equate the exponents:
[tex]\[
n = 4
\][/tex]
So, the solution to the equation [tex]\( 6 \times 10^n = 60000 \)[/tex] is [tex]\( n = 4 \)[/tex].
