Question

Find the value of (log2 8 + log3 9 + log5 25).​

Answer 1

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Find the value of (log2 8 + log3 9 + log5 25).

$\huge\underline\mathbb{\red S\pink{O}\purple{LU} \blue{T} \orange{IO}\green{N :}}$

★ Given that,

• Value of log2 8 + log3 9 + log5 25

★ So,

$\sf\:⟹ log \: _{2} \: 8 + log \: _{3} \: 9 + log \: _{5} \: 25$

$\sf\:⟹ log \: _{2} \: 2³ + log \: _ {3} \: 3² + log \: _{5} \: 5²$

• $\tt\: [↪ log \: _{x} \: mⁿ = n \: log \: _{x} \: m]$

$\sf\:⟹ 3 \: log \: _{2} \: 2 + 2 \: log \: _{3} \: 3 + 2 \: log \: _{5} \: 5$

• $[\tt\:↪ log \: _ {a} \: a = 1]$

$\sf\:⟹ 3(1) + 2(1) + 2(1)$

$\sf\:⟹ 3 + 2 + 2$

$\sf\:⟹ 7$

$\underline{\boxed{\bf{\purple{ ∴ Hence, \: the\:value\:of\: log\:_{2}\:8 + log\:_{3}\:9 + log\:_{5}\:25 = 7 }}}}$