evaluate the logarithm to 2 decimal places

Question

log_2.97.5

Answer 1

One way to do this problem is to use the change of base formula, which is 

 

log_ab = log₁₀(b) / log₁₀(a) 

 

So log_2.97.5 = log₁₀(7.5) / log₁₀(2.9) = 0.875061263 / 0.462397997 = 1.89244172

 

Another way to solve the problem is to set up a logarithmic equation and then rewrite it as a exponential equation  

 

x = log_2.97.5  ==>  

2.9^x = 7.5  

log₁₀2.9^x = log₁₀7.5

x*log₁₀2.9 = log₁₀7.5 

x = log₁₀(7.5) / log₁₀(2.9) = 1.89244172  

 

Check:  2.9^1.89244172 = 7.49999998 ~ 7.5