### Home > PC > Chapter 4 > Lesson 4.1.4 > Problem4-61

4-61.

Solve the following equations.

1. $50x^{2/3} = 100$

Divide both side by $50$ first.
Then undo the powers on both sides.

$(x^{2/3})^{3/2}= 2^{3/2}$

1. $\text{log}_3(x + 1) +\text{log}3(x) =\text{log}_3 12$

Combine the terms on the left side into one log.

$\text{log}_3((x + 1)(x)) =\text{log}_312$
$(x + 1)(x) = 12$

1. $50(\frac { 2 } { 3 })^x = 100$

Divide by $50$ first.
Then take the log of both sides, bringing the $x$ down in front.
Solve for $x$.

1. $\text{log}_3(x + 1) −\text{log}_3(x) =\text{log}_3 12$

This problem is similar to part (b).