SOLVE EQUATION FOR X: log 27^81=x the 27 is below the letter g on log?

If you mean log base 27 (81) = x

x = 4/3

loga of b = logk of b / logk of a .

k is a new base and can be any number.

Therefore, log27 of 81 = logk of 81 / logk of 27 = log 81 / log 27 = x

Use a calculator to tally log 81 / log 27 = 4/3

Then x=4/3.

Note: logarithms are exponents. So log27 81 = x means: what exponent x should you elevate 27 to get 81.

The exponent is x = 4/3. 27^(4/3) = 81

log[27] 81 = x

Hint: [27] is the base.

=> In logarithms, log[a] b = c in index form is b = a^c, then by applying this rule, you'll have

81 = 27^x

=> 81 & 27 in index forms are 3⁴ & 3³ respectively, then

3^4 = 3^3(x)

=> Cancel the integer: 3, from both sides, and you'll have

4 = 3x

4/3 = x

Hence x = 4/3 ...Ans.

81-27

27^X=81

3^3x=3^4

3x=4

x=4/3

Use the change of base formula

log_27(81) = log_3(81)/log_3(27) = log_3(3^4)/log_3(3^3) = 4/3

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