To solve the inequalities, we first need to convert them into exponential form and then solve for x.
1) Log2(x-3) < 1This can be rewritten as:2^(log2(x-3)) < 2^1x-3 < 2x < 5
Therefore, the solution to the first inequality is x < 5.
2) Log8(5x-3) < 2This can be rewritten as:8^(log8(5x-3)) < 8^25x-3 < 645x < 67x < 67/5
Therefore, the solution to the second inequality is x < 67/5.
In conclusion, the solutions to the given inequalities are x < 5 and x < 67/5.
To solve the inequalities, we first need to convert them into exponential form and then solve for x.
1) Log2(x-3) < 1
This can be rewritten as:
2^(log2(x-3)) < 2^1
x-3 < 2
x < 5
Therefore, the solution to the first inequality is x < 5.
2) Log8(5x-3) < 2
This can be rewritten as:
8^(log8(5x-3)) < 8^2
5x-3 < 64
5x < 67
x < 67/5
Therefore, the solution to the second inequality is x < 67/5.
In conclusion, the solutions to the given inequalities are x < 5 and x < 67/5.