To solve this inequality, we can start by simplifying both sides of the inequality:
0.7^(x^2 + 2x) < 0.7^3
Using the property of exponents that states a^(m+n) = a^m * a^n, we can rewrite the left side of the inequality as:
0.7^x^2 * 0.7^2x < 0.7^3
Now, let's simplify the exponents on the left side of the inequality:
0.7^x^2 * 0.7^2x = 0.7^(x^2 + 2x)
So, the inequality simplifies to:
0.7^(x^2 + 2x) < 0.7^3
Which is the same as the original inequality. Since the exponents are the same on both sides, we can conclude that this inequality will hold true for all x values.
To solve this inequality, we can start by simplifying both sides of the inequality:
0.7^(x^2 + 2x) < 0.7^3
Using the property of exponents that states a^(m+n) = a^m * a^n, we can rewrite the left side of the inequality as:
0.7^x^2 * 0.7^2x < 0.7^3
Now, let's simplify the exponents on the left side of the inequality:
0.7^x^2 * 0.7^2x = 0.7^(x^2 + 2x)
So, the inequality simplifies to:
0.7^(x^2 + 2x) < 0.7^3
Which is the same as the original inequality. Since the exponents are the same on both sides, we can conclude that this inequality will hold true for all x values.