Find N if log base 6 (6^7.8)=N
Solve the following inequality in terms of natural logarithms (ln).
(e^6x)+2 is less than or equal to 3.
To find the value of N in the equation log base 6 (6^7.8) = N, we need to understand the properties of logarithms.
In this case, the logarithm with base 6 is applied to the expression 6^7.8. Let's break it down step by step:
Step 1: Simplify the expression 6^7.8.
The exponent 7.8 can be written as a fraction, 39/5. So, using the exponentiation rule, we have:
6^7.8 = 6^(39/5).
Step 2: Apply the logarithm.
The logarithm of a number to a certain base is the exponent to which the base must be raised to obtain that number. In this case, we want to find the logarithm of 6^(39/5) with base 6.
Since 6^(39/5) equals 6 raised to an exponent of 39/5, which is equal to 7.8, the logarithm of 6^(39/5) to base 6 is equal to 7.8.
Therefore, N = 7.8.