This document contains a series of math and logic problems presented by Julio Núñez Cheng from Universidad Católica Los Ángeles de Chimbote. The problems cover various topics in algebra including equations, logarithms, exponents, and square roots. Solutions are provided for problems such as calculating pH from hydrogen ion concentration, solving multi-step logarithmic equations, finding square roots, and evaluating logarithmic and exponential expressions.

1. Universidad Católica Los Ángeles Matemática y Lógica
de Chimbote
Mg. Julio Núñez Cheng 1
= ↔ =
100 = 2 ↔ 100 = 10
64 = 3 ↔ 64 = 4
0,001 = −3 ↔ 0,001 = 10
32 = 5 ↔ 32 = 2
1
1
= 1 ↔ =
1
1 = 0 ↔ 1 =
1
( )( ) = +
= ↔ = … (1)
= ↔ = … (2)
(1) (2)

2. Universidad Católica Los Ángeles Matemática y Lógica
de Chimbote
Mg. Julio Núñez Cheng 1
=
= … (3)
( )( ) = +
,
( )( ) = +
= −
(1) (2) .
=
. . . …
= . . . … = + + + =
=
√ =
= 2,718 … 2.
log 57 = 1,756 ln 57 = 4,04
[H ]

3. Universidad Católica Los Ángeles Matemática y Lógica
de Chimbote
Mg. Julio Núñez Cheng 1
pH = log
1
[H ]
pH = log 1 − log [H ]
log 1 = 0 resulta pH = −log[H ]
pH
pH
HCl 0,01 M
pH = − log 0,01
pH = 2
pH = 1,35
pH = − log[H ]
1,35 = − log[H ]
−1,35 = log[H ]
[ ] = − 1,35
[ ] = 0,045
log( − 4) + log( + 4) = log 9

4. Universidad Católica Los Ángeles Matemática y Lógica
de Chimbote
Mg. Julio Núñez Cheng 1
log( − 4)( + 4) = log 9
log( − 4)( + 4) = log 9
( − 4)( + 4) = 9
− 16 = 9
= 25
= 5
= −5
log(2 + 4) − log( − 6) = log 8
(2 + 4)
( − 6)
= log 8
( )
( )
= log 8
(2 + 4)
( − 6)
= 8
= 8,67
[H ] = 0,025 M
pH = 0,015 [H ]?
[H ] = 0,97 M
log ( + 3 + 12) = 2
= 8
√ 32 =
= 10
2 log = log(6 + 7)
= 7 = −1

5. Universidad Católica Los Ángeles Matemática y Lógica
de Chimbote
Mg. Julio Núñez Cheng 1
log( + 10) − log(2 + 5) = log( − 4)
= 5 = −1
= 2√2
=