Question

Which equation can be used to find the solution of ((1)/(3))^(d-5)=81 ? Responses d + 5 = 4 d, + 5 = 4 -d+5=4 negative d plus 5 equals 4 d-5=4 d minus 5 equals 4 -d-5=4

Answer 1

To find the solution to the equation ((1)/(3))^(d-5) = 81, we can use logarithms. Take the logarithm of both sides with the same base, in this case base 3, to isolate the exponent. Then simplify the equation and solve for the variable d.

Step-by-step explanation:

To find the solution to the equation ((1)/(3))^(d-5) = 81, we need to start by isolating the base on one side of the equation. We can do this by taking the logarithm of both sides with the same base. In this case, we will use the logarithm base 3, since the base of the exponent is 3.

So, we have log base 3 of ((1)/(3))^(d-5) = log base 3 of 81. The logarithm of the exponent on the left side simplifies to (d-5) times the logarithm base 3 of 1/3. And the logarithm of 81 base 3 is equal to 4.

Therefore, we have (d-5) times logarithm base 3 of 1/3 = 4. This equation can now be solved for d using algebraic methods, such as isolating the variable d and simplifying the expression.

Answer 2

The equation that can be used to find the solution is d - 5 = 4.

Step-by-step explanation:

An equation is a mathematical statement asserting the equality of two expressions. It consists of an equal sign (=) between the expressions. Solving an equation involves determining the values of the variables that make the equation true, satisfying the equality condition.

To find the solution for the equation
`((1/3)^(d-5)=81,` we need to manipulate the equation to isolate the variable 'd'.

Step 1: Rewrite 81 as a power of 3. 81 =
`3^4.`

Step 2: Set the exponents equal to each other. d - 5 = 4.

Step 3: Solve for 'd' by adding 5 to both sides. d = 9.

Therefore, the equation that can be used to find the solution is d - 5 = 4.