If-2-a-5-3-b-9-and-25-c-8-Find-a-b-c-

Question Number 207250 by hardmath last updated on 10/May/24

If 2^{a} = 5, 3^{b} = 9 and 25^{c} = 8

Find : a \cdot b \cdot c = ?

Answered by A5T last updated on 10/May/24

a = {l o g}_{2} 5; b = 2; c = {l o g}_{25} 8 = \frac{1}{2} {l o g}_{5} 8 = {l o g}_{5} (2 \sqrt{2})

\Rightarrow a b c = 2 {l o g}_{2} 5 \times {l o g}_{5} 2 \sqrt{2} = {l o g}_{2} 8 = 3

Commented by hardmath last updated on 10/May/24

thank you dear professor

Answered by Rasheed.Sindhi last updated on 11/May/24

3^{b} = 9 \Rightarrow 3^{b} = 3^{2} \Rightarrow b = 2

2^{a} = 5 \Rightarrow 2 = 5^{\frac{1}{a}}

25^{c} = 8 \Rightarrow 5^{2 c} = 2^{3} = {(5^{\frac{1}{a}})}^{3}

\Rightarrow 5^{2 c} = 5^{\frac{3}{a}} \Rightarrow 2 c = \frac{3}{a} \Rightarrow ac = \frac{3}{2}

(ac) (b) = \frac{3}{2} (2) = 3 \Rightarrow abc = 3