How do you solve $9^(x+1) = 27$ ?

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Answer 1 · 2016-04-12T01:48:09

$x = 1/2$

We will use the following properties:

$9^(x+1) = 27$

$=> log_3(9^(x+1)) = log_3(27)$

$=>(x+1)log_3(9) = log_3(27)$

$=>(x+1)log_3(3^2) = log_3(3^3)$

$=>2(x+1) = 3$

$=>x+1 = 3/2$

$:. x = 1/2$

Answer 2 · 2016-04-12T01:51:08

Alternative solution:

You can write everything in the same base:

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

$3^(2x + 2) = 3^3$

$3^(2x) = 3^(3 - 2)$

$3^(2x) = 3^1$

$2x = 1$

$x = 1/2$

Hopefully this helps!

How do you solve 9^(x+1) = 279^(x+1) = 27?