Question

a) rewrite the equation below using the common base of 3. 3^x+3 × (1/9)^x-1 = 13 __(select) ____ x 3 __(select) ____ = 3 __(select) ____b) Apply the same base rule and solve for x. x = ______

Answer 1

we have 3^x +3 x (1/9)^x-1 = 1

Remember 3 is a factor of 9 and 9 = 3^2

Therefore, 1/9 = 1/3^2

we can rewrite the above equation as

3^x + 3 x (1/3^2)^x-1 = 1

We have some rule of indicies guiding this equation

x^-a = 1/x^a

this means that 1/3^2 can also be written as 3^-2

i.e 1/3^2 = 3^-2

put 3^-2 to replace 1/3^2

= 3^x + 3 x (3^-2)^x-1 = 1

Let us check another rule

x^0 = 1

3^x + 3^1