Question

Logarithm of 32 5 root 4 to the base 2 root 2 is

Answer 1

Logarithm of 32 5 root 4 to the base 2 root 2 is 3.6

Step-by-step explanation:

Logarithm of 32 5 root 4 to the base 2 root 2 is written as:

$\log _{2\sqrt{2}} 32 \times 4^{1 / 5}$

The logarithmic formula used is:

$\log _{b} a^{N} \Rightarrow N \log _{b}{a}$

$\log _{b^{N}} a \Rightarrow \frac{1}{N} \log _{b} a$

On applying the formula, we get,

⇒ 32 × 4¹⁾⁵ = 2⁵ × 2²⁾⁵ = 2⁽² ⁺ ²⁾⁵⁾ = 2²⁷⁾⁵

⇒ 2√2 = 2 · 2¹⁾² = 2⁽¹ ⁺ ¹⁾²⁾ = 2³⁾²

Now,

$\log _{2\sqrt{2}} 32 \times 4^{1 / 5}$ = $\log_{2^{3/2}}2^{27/5}$ = (27/5 $\times \log_{2^{3/2}}2$)

⇒ 27/5 × 2/3 log₂2 = 3.6 × log₂2

∵ log₂2 = 1

3.6 × log₂2 = 3.6 × 1 = 3.6

∴ $\log _{2\sqrt{2}} 32 \times 4^{1 / 5}$ = 3.6

Answer 2

Step-by-step explanation:

see attachment

answer 3.6