Question

Solve it

$\boxed{\sf log_432=?}$​

Answer 1

$\huge{\sf log_432=?}$

4 raised to power x is 32.

${4}^{x} = 32$

For. eg.)

${2}^{3} = {2}^{x}$

➝ x = 3

__________________________________

For 4,

${4}^{1} = 4$

${4}^{2} = 4 \times 4 = 16$

${4}^{3} = 4 \times 4 \times 4 = 16 \times 4 = 64$

For 2,

[tex] {2}^{1} = 2[/tex]

${2}^{2} = 2 \times 2 = 4$

${2}^{3} = 2 \times 2 \times 2 = 4 \times 2 = 8$

${2}^{4} = 2 \times 2 \times 2 \times 2 = 4 \times 4 = 16$

${2}^{5} = 2 \times 2 \times 2 \times 2 \times 2 = 4 \times 4 \times 2 = 16 \times 2 = 32$

__________________________________

$\huge{\sf log_432}$

➝ ${4}^{x} = 32$

➝ ${2}^{2x} = {2}^{5}$

➝ 2x = 5

➝ x = 5/2

➝ x = 2.5

__________________________________

Answer 2

Given: $\boxed{\sf log_432}$

To find: The value of ${\sf log_432}$.

Solution: To find the value of ${\sf log_432}$. Let us consider its value to be x, thus we can write that:

${\sf log_432=}$ x

Now this equation can be written as:

4^x = 32

This can also be written as:

2^(2x) = 2⁵

Since the base are same, we can compare the powers. On comparing the powers we get:

2x = 5

x = 5/2

x = 2.5

Thus the value of ${\sf log_432}$ came out to be 2.5.