Actually, you can make the bases equal.Shyan said:You can't make the bases equal because [itex] 81=3^4 [/itex] and [itex] 32=2^5 [/itex].
To the OP:Shyan said:You should solve [itex] 81^5=32^x [/itex] for x. That'll be the maximum value! Just get the logarithm(in any base) of both sides. That'll get out x in a way that you can isolate it.
Try to make the bases on both sides of the inequality same.
Inequalities with exponents involve expressions with variables raised to a power, such as x^2 or 2^x. These inequalities compare two expressions using symbols like <, >, ≤, and ≥.
To solve an inequality with exponents, isolate the variable on one side of the inequality sign and use inverse operations to solve for the variable. Keep in mind that you may need to use properties of exponents, such as multiplying or dividing both sides by the same base, to simplify the expressions.
The process for maximizing x in an inequality with exponents involves finding the maximum value of x that satisfies the inequality. This can be done by solving the inequality and then checking the values of x that make the inequality true.
Inequalities with exponents are commonly used in real-world situations, such as in finance and economics, to model relationships between variables. Understanding how to solve these types of inequalities allows us to make accurate predictions and decisions based on these models.
- When raising a number or variable to a negative power, remember to take the reciprocal of the base.
- When multiplying or dividing both sides of an inequality by a negative number, remember to flip the inequality sign.
- Break down complex expressions into simpler ones using properties of exponents.
- Check the solution by plugging it back into the inequality and making sure it satisfies the inequality.