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Sagot :
If [tex]10^{4}[/tex]= 10,000, then the value of 4 = [tex]log_{10}[/tex] 10000. and the equation equivalent to [tex]a^{5}[/tex] = 21 is 5 = [tex]log_{a}[/tex] 21.
The logarithm is the exponent or power to which a base must be raised to yield a given number. Expressed mathematically, x is the logarithm of n to the base b if [tex]b^{x}[/tex] = n, which can be written as x = [tex]log_{b}[/tex] n.
For example, [tex]2^4[/tex] = 16; therefore, 4 is the logarithm of 8 to base 2, or 4 = [tex]log_{2}[/tex] 8.
a. Here, 4 is the power of the 10, and we will express it in the log form. 4, is the logarithm of 10000 to base 10 or mathematically we can express it as -
4 = [tex]log_{10}[/tex] 10000.
b. Similarly, we have to find the equation equivalent to [tex]a^{5}[/tex] = 21
using the log form, we get that 5 is the logarithm of 21 to base a.
Mathematically we can express it as -
5 = [tex]log_{a}[/tex] 21.
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The complete question is -
If [tex]10^{4}[/tex] = 10,000, which is equal to 4? Which equation is equivalent to [tex]a^{5}[/tex] = 21?
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