- #1
Mphisto
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Homework Statement
Solve the equation
7^2x+3 / 7^x^2 = 1
Homework Equations
The Attempt at a Solution
How can i "breakdown" 7^x^2? Thank you!
AlchemistK said:Are you sure breaking down 7^x^2 is the only way?
Try cross multiplying it to the other side and observe.
Is the numerator supposed to be 72x + 3 or 72x + 3 or 72x + 3?Mphisto said:Homework Statement
Solve the equation
7^2x+3 / 7^x^2 = 1
Mphisto said:Homework Equations
The Attempt at a Solution
How can i "breakdown" 7^x^2? Thank you!
Mphisto said:Solve the equation
7^2x+3 / 7^x^2 = 1
.
.
.
How can i "breakdown" 7^x^2? Thank you!
checkitagain said:And, to be unambiguous, type "7^(x^2)"
if you mean [itex]7^{x^2}.[/itex]
The first step is to rewrite the equation in a more simplified form by using the laws of logarithms. We can rewrite 7^2x+3 as (7^x)^2 * 7^3 and 7^x^2 as (7^x)^2. This will give us the equation (7^x)^2 * 7^3 = (7^x)^2.
After rewriting the equation, we can cancel out the common term of (7^x)^2 on both sides. This will leave us with 7^3 = 1. We know that any number raised to the power of 0 is equal to 1, so we can rewrite this as 7^3 = 7^0. Therefore, x must equal 0.
Yes, there may be other solutions depending on the initial values of x. For example, if x = 1, the equation would become 7^5 = 7^1, which is also a valid solution. However, if we plug in any other value for x, the equation will not hold true.
The steps for solving this equation would be similar. We would rewrite the equation as (7^x)^2 * 7^3 = (8^x)^2 and then cancel out the common terms of (7^x)^2 and (8^x)^2. This would leave us with 7^3 = 8^3, and we can solve for x from there.
No, in order to solve this equation, we need to use the laws of logarithms to simplify it and then solve for x. Without using logarithms, it would be difficult to cancel out the common terms and solve for x.