Question

If a2 = b3 = c5 = d 6 , the value of logd (abc) is
​

Answer 1

Answer:

a + b whole square is equal to a into b

Answer 2

if a² = b³ = c⁵ = d⁶   then $\log_{d}(abc)$  is $\dfrac{31}{5}$

Given:

• a² = b³ = c⁵ = d⁶

To Find:

• $\log_{d}(abc)$

Solution:

• (xᵃ)ᵇ = xᵃᵇ
• xᵃ.xᵇ=xᵃ⁺ᵇ
• logₐa = 1
• logaⁿ = n log a

Step 1:

Assume that

a² = b³ = c⁵ = d⁶  = k³⁰

Hence

a = k¹⁵

b = k¹⁰

c =k⁶

d = k⁵

Step 2:

Find abc

k¹⁵.k¹⁰.k⁶

= k³¹

$=(k^5)^{\frac{31}{5} }$

Step 3:

$\log_{d}(abc) = \log_{k^5}( (k^5)^{\frac{31}{5} })$

$=\frac{31}{5} \log_{k^5}( k^5 })$

= 31/5

 

Hence if a² = b³ = c⁵ = d⁶   then $\log_{d}(abc)$  is $\dfrac{31}{5}$