a. log2√32 = log2 + log√32 = 1 + log2⁵/² = 1 + 5/2log2 = 1 + 5/2 = 7/2
² ² ² ² ²
b. log∛3·27 = log∛3 + log27 = log3¹/³ + log3³ =1 /3log3 + 3log3 =1/3 + 3 =
³ ³ ³ ³ ³ ³ ³
=10/3
d. log ( log625) = log(log5⁴) = log(4log5) = log(4· 2 ) = log2³ = 3log2 = 3·3=9
∛2 ∛2 ∛2 ∛2 ∛2 ∛2
log5 = 1 / log√5 = 1 / log5¹/² = 1 / [ 1 /2 log5 ] = 2
⁵ ⁵ ⁵ ⁵
log2 = 1 / log∛2 = 1 / log2¹/³ = 1 / [ 1/3 log2 ] = 3
∛2 ² ² ²
d. (3 ) ( la putrea log 5 ) = 5 ; 2( la puterea log 3 ) = 3
³ ²
ex = 5 + 3 = 8
f. log25 = log5² = 2log5
⁴ ⁴ ⁴
2 ( la puterea 2log5) = ( 2² ) ( la puterea log5 ) = 4 ( la log5) = 5
⁴ ⁴ ⁴
4 ( la log9) =( 2 ²) ( la log9 ) = 2 ( la 2log9) = 2 ( la log9²) = 9² = 81
² ² ² ²
ex = 5 + 81 = 86
i. log12 + log5 - log10 = log[( 12 · 5 ) : 10] = log6 = 1
⁶ ⁶ ⁶ ⁶ ⁶
