Solve 1 * 10^(6/x) = 1000
10^0×10^(x/6)=10³
10^(0+x/6)=10³
10^(x/6)=10^3
X/6=3
X=6×3
take log of both sides
log (10^(6/x) = log 1000
(6/x)log10 = log1000
6/x = 3
3x = 6
x = 2
Missed read the question
Thank you sir reiny
(6/x)=3
6=3x
X=2
To solve the equation 1 * 10^(6/x) = 1000, we need to isolate the variable x. Here's how to do it:
Step 1: Divide both sides of the equation by 1 to simplify it:
1 * 10^(6/x) / 1 = 1000 / 1
Step 2: Rewrite the equation using exponent properties. Since 10^(a - b) = 10^a / 10^b, we can rewrite 10^(6/x) as 10^6 / 10^x:
10^6 / 10^x = 1000
Step 3: Simplify further by reducing the powers of 10. Since 10^6 = 1,000,000 and 10^x = 1000, we have:
1,000,000 / 10^x = 1000
Step 4: Convert both sides of the equation to the same base. Since both sides have powers of 10, we can rewrite 1000 as 10^3:
1,000,000 / 10^x = 10^3
Step 5: Rewrite 1,000,000 as 10^6 to have a common base:
10^6 / 10^x = 10^3
Step 6: Use exponent properties to simplify the left side. Since 10^a / 10^b = 10^(a - b), we have:
10^(6 - x) = 10^3
Step 7: Since the bases are equal, the exponents must be equal as well:
6 - x = 3
Step 8: To isolate x, subtract 6 from both sides:
-x = 3 - 6
Step 9: Simplify:
-x = -3
Step 10: To solve for x, multiply both sides of the equation by -1:
x = -(-3)
Step 11: Simplify:
x = 3
Therefore, the solution to the equation 1 * 10^(6/x) = 1000 is x = 3.