Question

Question #53d49

Answer 1

Given: `3(2)^(x-1) = 24`

Divide both sides by 3:

`2^(x-1)=8`

We know that `8 = 2^3`:

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

Set the exponents equal:

`x-1 = 3`

`x = 4 larr` answer

Answer 2

`x=4`

Explanation:

Isolate the exponent and solve using logs.

Firstly divide both sides by 3.

`2^(x-1) = 24/3 = 8`

Now, we can take Logs of both sides:

`ln(2^(x-1)) = ln(8)`

Using the log property `ln a^b = blna`, we get:

`(x-1)ln2 = ln8`

Isolate the `x`:

`x-1 = ln8/ln2`

Thus, `x = ln8/ln2 + 1 = 3 + 1`
`x = 4`

Answer 3

`x=4`

Explanation:

Step 1. Divide both sides by `3`

`(cancel(3)(2)^(x-1))/(cancel(3))=24/3`

`2^(x-1)=8`

Step 2. Take the logarithm of both sides.

`log(2^(x-1))=log(8)`

Step 3. Use the power rule of logarithms, `log(a^x)=xlog(a)`

`(x-1)log(2)=log(8)`

Step 4. Divide both sides by `log(2)`

`((x-1)cancel(log(2)))/cancel(log(2))=log(8)/log(2)`

`x-1=log(8)/log(2)`

`x=1+log(8)/log(2)`

Step 5. Express `8=2^3` and use power rule again to simplify

`x=1+log(2^3)/log(2)`

`x=1+(3log(2))/log(2)`

`x=1+(3cancel(log(2)))/cancel(log(2))`

`x=1+3=4`