Log²10= 0.3010 and log³10= 0.4771
The given logarithmic equations are correct.
To calculate log₂10, we need to determine the exponent to which we need to raise 2 to obtain 10. In other words, we need to find the value of x in the equation 2^x = 10.
We know that 2³ = 8, and 2⁴ = 16. Since 10 is between 8 and 16, we can estimate that x should be a little larger than 3 but less than 4.
Using the logarithmic property log_b(a) = c, we can rewrite the equation 2^x = 10 as log₂10 = x.
To calculate log₂10 more precisely, we can use a logarithm calculator or a scientific calculator with a logarithm function. The exact value of log₂10 is approximately 3.3219.
Similarly, to calculate log₃10, we need to determine the exponent to which we need to raise 3 to obtain 10. In other words, we need to find the value of y in the equation 3^y = 10.
Since 3² = 9 and 3³ = 27, we know that y should be between 2 and 3. We can estimate that y is approximately 2.5.
Using the logarithmic property log_b(a) = c, we can rewrite the equation 3^y = 10 as log₃10 = y.
To calculate log₃10, we can use a logarithm calculator or a scientific calculator with a logarithm function. The exact value of log₃10 is approximately 2.0959.