Question

Write as one problem: log3 8x + log3 4 = 2

Answer 1

`x = (9)/(32)`

Explanation:

`\log_3(8x) + \log_3(4) = 2`

We can rewrite this equation using the log addition rule:

`\log_b(x) + \log_b(y) = \log_b(xy)`

`\log_3(8x\cdot 4)= 2`

`\log_3(32x)= 2`

Then, we can put both sides of the equation inside the exponent of 3.

`3^(\log_3(32x)) = 3^2`

`32x = 9`

From here, we can divide both sides by 32 to solve for x.

`\boxed{x = (9)/(32)}`