Buy converting to exponential form find the value of the following i. log8 32 ii. log2 (0.125)?

Question

Answer

Converting Logarithmic to Exponential Form

i. log8 32
To convert the logarithmic expression log8 32 to exponential form, we need to remember that logarithmic form can be written as loga b = x is equivalent to a^x = b. Therefore, log8 32 can be written as 8^x = 32. Now, we need to find the value of x that satisfies this equation.
8^x = 32
2^3^x = 2^5
3^x = 5
Thus, the exponential form of log8 32 is 3^x = 5.

ii. log2 (0.125)
Similarly, to convert the logarithmic expression log2 (0.125) to exponential form, we can rewrite it as 2^x = 0.125. We need to express 0.125 as a power of 2 in order to find the value of x.
2^x = 0.125
2^x = 2^-3
x = -3
Therefore, the exponential form of log2 (0.125) is 2^-3.

In conclusion, by converting the given logarithmic expressions to exponential form, we have found the respective values of x that satisfy the equations. This process helps in understanding the relationship between logarithmic and exponential forms of expressions.

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