Answer :

To find the value of [tex]\( t \)[/tex] in the equation [tex]\( 7000 = 7 \times 10^t \)[/tex], follow these steps:

1. Isolate [tex]\( 10^t \)[/tex]:
We start with the equation:
[tex]\[
7000 = 7 \times 10^t
\][/tex]
To isolate [tex]\( 10^t \)[/tex], divide both sides by 7:
[tex]\[
10^t = \frac{7000}{7}
\][/tex]

2. Simplify the division:
Calculate [tex]\( \frac{7000}{7} \)[/tex] to simplify the right side:
[tex]\[
\frac{7000}{7} = 1000
\][/tex]
So now we have:
[tex]\[
10^t = 1000
\][/tex]

3. Solve for [tex]\( t \)[/tex]:
To find [tex]\( t \)[/tex], recognize that 1000 is a power of 10. Specifically:
[tex]\[
1000 = 10^3
\][/tex]
This means that:
[tex]\[
10^t = 10^3
\][/tex]
Therefore, [tex]\( t = 3 \)[/tex].

Thus, the value of [tex]\( t \)[/tex] is [tex]\( 3 \)[/tex].

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Rewritten by : Barada