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Answer :
To solve the exponential equation [tex]\(5^{3x-10} = 3125\)[/tex], follow these steps:
1. Understand the bases: Look at the number 3125 and see if you can express it as a power of 5. After checking, you find that [tex]\(3125 = 5^5\)[/tex].
2. Set the exponents equal: Since the bases on both sides of the equation are the same (both are base 5), you can set the exponents equal to each other:
[tex]\[
3x - 10 = 5
\][/tex]
3. Solve for [tex]\(x\)[/tex]:
- First, add 10 to both sides of the equation to isolate the term with [tex]\(x\)[/tex]:
[tex]\[
3x = 5 + 10
\][/tex]
- Simplify the right side:
[tex]\[
3x = 15
\][/tex]
- Finally, divide both sides by 3 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{15}{3}
\][/tex]
- Simplify the division:
[tex]\[
x = 5
\][/tex]
So, the solution to the equation is [tex]\(x = 5\)[/tex].
1. Understand the bases: Look at the number 3125 and see if you can express it as a power of 5. After checking, you find that [tex]\(3125 = 5^5\)[/tex].
2. Set the exponents equal: Since the bases on both sides of the equation are the same (both are base 5), you can set the exponents equal to each other:
[tex]\[
3x - 10 = 5
\][/tex]
3. Solve for [tex]\(x\)[/tex]:
- First, add 10 to both sides of the equation to isolate the term with [tex]\(x\)[/tex]:
[tex]\[
3x = 5 + 10
\][/tex]
- Simplify the right side:
[tex]\[
3x = 15
\][/tex]
- Finally, divide both sides by 3 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{15}{3}
\][/tex]
- Simplify the division:
[tex]\[
x = 5
\][/tex]
So, the solution to the equation is [tex]\(x = 5\)[/tex].
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