Answer :

Sure! Let's work through the question step-by-step to find the value of [tex]\( t \)[/tex] in the equation [tex]\( 7000 = 7 \times 10^t \)[/tex].

1. Understand the Equation: We have [tex]\( 7000 = 7 \times 10^t \)[/tex]. Here, we want to isolate [tex]\( 10^t \)[/tex].

2. Divide Both Sides by 7: To get [tex]\( 10^t \)[/tex] by itself, divide both sides of the equation by 7.

[tex]\[
\frac{7000}{7} = \frac{7 \times 10^t}{7}
\][/tex]

Simplifying both sides, we get:

[tex]\[
1000 = 10^t
\][/tex]

3. Solve for [tex]\( t \)[/tex]: We now have the equation [tex]\( 1000 = 10^t \)[/tex]. We need to find [tex]\( t \)[/tex] such that [tex]\( 10^t = 1000 \)[/tex].

4. Recognize the Power of 10: Notice that 1000 can be written as a power of 10. Specifically, [tex]\( 1000 = 10^3 \)[/tex], since:

[tex]\[
10^3 = 10 \times 10 \times 10 = 1000
\][/tex]

5. Conclude the Solution: Since [tex]\( 10^t = 10^3 \)[/tex], it follows that [tex]\( t = 3 \)[/tex].

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

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Rewritten by : Barada