mathematically Evaluate without using tables 2 log base 10 raised 2 power 5 + log base 10 36 - log base10 9 that is, 2log10 5 +log 10 36 - log 10 9
The words are confusing, but it appears that you have
2log5 + log36 - log9
= log(25*36/9)
= log100
= 2
Rather than trying to toss in all those a0's, just say at the start that all logs are base 10.
True Steve. I searched. It's confusing to me too.
To evaluate the expression 2 log base 10 (2^5) + log base 10 (36) - log base 10 (9), we can use logarithmic properties:
1. Recall the logarithmic property: log base a (b^c) = c log base a (b).
Using this property, we can simplify the expression:
2 log base 10 (2^5) + log base 10 (36) - log base 10 (9)
= 2(5) log base 10 (2) + log base 10 (36) - log base 10 (9)
= 10 log base 10 (2) + log base 10 (36) - log base 10 (9)
2. Now, let's simplify further.
log base 10 (2) represents the exponent to which we raise 10 to get 2. Since 10^1 = 10, we have log base 10 (2) = 1.
Therefore, the expression becomes:
10(1) + log base 10 (36) - log base 10 (9)
= 10 + log base 10 (36) - log base 10 (9)
3. Next, simplify the logarithms:
log base 10 (36) represents the exponent to which we raise 10 to get 36. Since 10^2 = 100, we have log base 10 (36) = 2.
log base 10 (9) represents the exponent to which we raise 10 to get 9. Since 10^1 = 10, we have log base 10 (9) = 1.
Therefore, the expression becomes:
10 + 2 - 1
4. Finally, solve the expression:
10 + 2 - 1 = 11
So, 2 log base 10 (2^5) + log base 10 (36) - log base 10 (9) is equal to 11.
To evaluate the expression 2log10(5) + log10(36) - log10(9) without using tables, we can use logarithmic properties and simplifications.
1. Start with the expression: 2log10(5) + log10(36) - log10(9).
2. Use the logarithmic property loga(b^n) = nloga(b) to simplify each term:
- 2log10(5) can be rewritten as log10(5^2) = log10(25).
- log10(36) remains the same.
- log10(9) remains the same.
3. Rewrite the expression: log10(25) + log10(36) - log10(9).
4. Use the logarithmic property loga(b) + loga(c) = loga(b * c) to combine the terms inside the parentheses:
- log10(25) + log10(36) - log10(9) can be rewritten as log10(25 * 36) - log10(9).
5. Simplify the multiplication inside the logarithm:
- 25 * 36 = 900.
6. Rewrite the expression: log10(900) - log10(9).
7. Use the logarithmic property loga(b) - loga(c) = loga(b / c) to combine the terms:
- log10(900) - log10(9) can be rewritten as log10(900 / 9).
8. Simplify the division inside the logarithm:
- 900 / 9 = 100.
9. Rewrite the expression: log10(100).
10. Finally, evaluate the logarithm base 10 of 100:
- log10(100) = 2.
So, the evaluated expression 2log10(5) + log10(36) - log10(9) is equal to 2.