Solution:

Given: log25 to the base 10–log2³ to the base 10 log4² to the base 10

Let's solve each term step by step.

1. log25 to the base 10
We know that 25 can be written as 5². Therefore,
log25 to the base 10 = log5² to the base 10
Using the formula loga^n = nloga, we get
log5² to the base 10 = 2log5 to the base 10
Now we can use the logarithmic table to find the value of log5 to the base 10 which is approximately 0.699.
Therefore, 2log5 to the base 10 = 2 x 0.699 = 1.398.

2. log2³ to the base 10
We know that 2³ = 8. Therefore,
log2³ to the base 10 = log8 to the base 10
Using the formula loga^n = nloga, we get
log8 to the base 10 = 3log2 to the base 10
Now we can use the logarithmic table to find the value of log2 to the base 10 which is approximately 0.301.
Therefore, 3log2 to the base 10 = 3 x 0.301 = 0.903.

3. log4² to the base 10
We know that 4² = 16. Therefore,
log4² to the base 10 = log16 to the base 10
Using the formula loga^n = nloga, we get
log16 to the base 10 = 2log4 to the base 10
Now we can use the logarithmic table to find the value of log4 to the base 10 which is approximately 0.602.
Therefore, 2log4 to the base 10 = 2 x 0.602 = 1.204.

Now we can substitute the values in the given expression.

log25 to the base 10 – log2³ to the base 10 + log4² to the base 10
= 1.398 – 0.903 + 1.204
= 1.699

Therefore, the value of the given expression is 1.699.