I suggest dividing by 3x .kaspis245 said:Homework Statement
##15(5^x-3^x)<16⋅15^{\frac{x}{2}}##
Homework Equations
Rules of logarithms
The Attempt at a Solution
I don't know where to start.
Here's one way to start rearranging the equation:
##5^x-3^x<16⋅15^{\frac{x-2}{2}}##
What's the correct way to start rearranging?
An exponent is a mathematical notation that represents repeated multiplication. It is written as a superscript number to the right of a base number, indicating how many times the base number should be multiplied by itself.
To solve a problem with exponents, you can use the rules of exponentiation. These rules include multiplying exponents with the same base, dividing exponents with the same base, and raising a power to a power.
A positive exponent represents repeated multiplication, while a negative exponent represents repeated division. For example, 23 = 2 x 2 x 2 = 8, while 2-3 = 1 / (2 x 2 x 2) = 1/8.
To simplify expressions with exponents, you can use the rules of exponentiation and the properties of exponents. These include the power rule, product rule, quotient rule, and zero and negative exponent rules.
Exponents are used in many scientific fields, such as physics and chemistry, to represent large or small quantities. They are also used in finance to calculate compound interest and in computer science to represent data sizes in bits and bytes.