Question

Solve each equation (Isolating first)


`3` ·
`((1)/(8))^(2x) = 12`


`2` ·
`(\sqrt[3]{5})^(4x) = 50`

Answer 1

`3 * {( (1)/(8) )}^(2x) = 12 \\ \Leftrightarrow {( (1)/(8) )}^(2x) = 4 \\ \Leftrightarrow {( {2}^( - 3)) }^(2x) = {2}^(2) \\ \Leftrightarrow {2}^( - 6x) = {2}^(2) \\ \Leftrightarrow - 6x = 2 \\ \Leftrightarrow x = - (1)/(3) \\ \\ 2 {\sqrt[3]{5}}^(4x) = 50 \\ \Leftrightarrow { \sqrt[3]{5} }^(4x) = 25 \\ \Leftrightarrow {5}^{ (4x)/(3) } = {5}^(2) \\ \Leftrightarrow (4x)/(3) = 2 \\ \Leftrightarrow 4x = 6 \\ \Leftrightarrow x = (3)/(2)`

Answer 2

Answer to Q1:

x= -1/3

Explanation:

We have given the equations.

We have to solve these equations.

The first equation is :

`3.((1)/(8))^(2x)`

`((1)/(8))^(2x)=4`

`(2^(-3x))^(2x)=4`

`2^(-6x)=4`

`2^(-6x)=2^(2)`

As we know that bases are same then exponents are equal.

-6x = 2

x = 2/-6

x=-1/3

Answer to Q2:

x = 3/2

Explanation:

The given equation is :

`2.\sqrt[3]{5}^(4x)=50`

We have to find the value of x.

First,we multiply both sides of equation by 1/2 we get,

`5^(4x/3)=25`

`5^(4x/3)=5^(2)`

4x/3=2

4x = 6

x = 3/2