Express $3^4=81$ in logarithmic form.

By the definition, $a^x=N \iff \log_a N=x$. Matching $3^4=81$ to this pattern: base $a=3$, exponent $x=4$, result $N=81$. $$3^4=81 \quad\Longleftrightarrow\quad \log_3 81 = 4$$ **Check (independent recomputation):** convert back — $\log_3 81=4$ means $3$ raised to the power $4$ should give $81$: $3\times3\times3\times3=9\times9=81$ ✓. > [!ANSWER] > $\log_3 81 = 4$

Express 3⁴=81 in logarithmic form.

Worked Examples · Example 1

3^4=81

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Concept understanding — Logarithm as the Inverse of Exponentiation

$\log_a N=x$ means exactly $a^x=N$ (for $a>0,a\neq1,N>0$ ) — a logarithm IS the exponent needed to turn the base $a$ into $N$ . $\log_a a=1$ and $\log_a 1=0$ hold for every valid base. A logarithm is undefined for a non-positive argument, since no real power of a positive base ever produces zero or a negative number.

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Q.Express 34=813^4=8134=81 in logarithmic form.

Concept understanding — Logarithm as the Inverse of Exponentiation

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Q.Express $3^4=81$ in logarithmic form.

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