If `log_(4)m=1.5`, then find the value of m.

Options

A. `5`
B. `6`
C. `10`
D. `8`

Explanation

To solve the problem where we need to find the value of \( m \) given that \( \log_{4} m = 1.5 \), we can follow these steps:

### Step 1: Rewrite the logarithmic equation in exponential form
The logarithmic equation \( \log_{4} m = 1.5 \) can be rewritten in its exponential form. This means that:
\[ m = 4^{1.5} \]

### Step 2: Simplify \( 4^{1.5} \)
We can express \( 4^{1.5} \) as follows:
\[ 4^{1.5} = 4^{\frac{3}{2}} = (4^{\frac{1}{2}})^3 \]

### Step 3: Calculate \( 4^{\frac{1}{2}} \)
The term \( 4^{\frac{1}{2}} \) represents the square root of 4:
\[ 4^{\frac{1}{2}} = \sqrt{4} = 2 \]

### Step 4: Raise the result to the power of 3
Now we can substitute back into our equation:
\[ m = (2)^3 \]

### Step 5: Calculate \( 2^3 \)
Finally, we calculate \( 2^3 \):
\[ m = 8 \]

Thus, the value of \( m \) is \( 8 \).

### Summary of Steps:
1. Rewrite the logarithmic equation in exponential form: \( m = 4^{1.5} \).
2. Simplify \( 4^{1.5} \) to \( (4^{\frac{1}{2}})^3 \).
3. Calculate \( 4^{\frac{1}{2}} = 2 \).
4. Raise the result to the power of 3: \( m = (2)^3 \).
5. Calculate \( 2^3 = 8 \).