Hello guys!
Could someone help me with this problem? Coz Ive been trying to solve this already for an hour but still I dont get it.
Heres the question, FInd the exact value of the given expression:
25^log58
Thanks in advanced.
Since the exponential function $\displaystyle f(x)=b^x$ and the logarithmic function $\displaystyle g(x)=\log_bx$ are inverses of each other, their composites are the identity function. That is,
$\displaystyle f[g(x)]=x \ \ and \ \ g[f(x)]=x$
$\displaystyle f(\log_bx)=x \ \ and \ \ g(b^x)=x$
$\displaystyle b^{\log_bx}=x \ \ and \ \ \log_bb^x=x$
Thus, if their bases are the same, exponential and logarithmic functions "undo" each other. You can use this inverse property of exponents and logarithms to simplify expression like yours.
$\displaystyle 25^{\log_58}=5^{(2)\log_58}$
Using $\displaystyle (p)\log_bm=\log_bm^p$, we get
$\displaystyle 5^{\log_58^2}=8^2=64$
I hope I've cleared up any confusion you may have had.