PSC, RRB, ADRE, Different Compitition Question Practice

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Prove that: 3log10^(2) + log10^(5) = log10^(40)

Solⁿ:

Left-hand side (LHS): 3log10^(2) + log10^(5)

Use the law: nlog a = log a^n

So,

3log10^(2) = log10^(2^3) = log10^(8)

Now LHS becomes: log10^(8) + log10^(5)

Use another log rule: log(M)+log(N) = log(MN)

So,

log10^(8) + log10^(5)

= log10^(8×5)

= log10​^(40)

This is the Right-hand side (RHS).