Rewrite the following exponential functions as logarithmic functions, and the logarithmic functions as exponential functions:
f(x)=(7/8)^x
b)
f(x)=log12x
c)
f(x)=log5/9x
a) The exponential function rewritten as a logarithmic function is:
log base (7/8) of f(x) = x.
The logarithmic function rewritten as an exponential function is:
f(x) = (7/8)^(log base (7/8) of x).
b) The logarithmic function rewritten as an exponential function is:
f(x) = 12^x.
The exponential function rewritten as a logarithmic function is:
log base 12 of f(x) = x.
c) The logarithmic function rewritten as an exponential function is:
f(x) = (5/9)^x.
The exponential function rewritten as a logarithmic function is:
log base (5/9) of f(x) = x.
a) Exponential function: f(x) = (7/8)^x
Rewritten as a logarithmic function: log(7/8, f(x))
b) Logarithmic function: f(x) = log12(x)
Rewritten as an exponential function: 12^f(x) = x
c) Logarithmic function: f(x) = log(5/9, x)
Rewritten as an exponential function: (5/9)^f(x) = x
To rewrite an exponential function as a logarithmic function, you need to use the following steps:
Step 1: Identify the base of the exponential function.
Step 2: Set the expression equal to y, as it represents the output (y-value) of the exponential function.
Step 3: Rewrite the equation in logarithmic form, using the base as the base of the logarithm and the exponent as the input (x-value) of the logarithmic function.
Now let's apply these steps to rewrite the exponential functions as logarithmic functions:
a) f(x) = (7/8)^x
Step 1: The base of the exponential function is 7/8.
Step 2: Set the expression equal to y: y = (7/8)^x.
Step 3: Rewrite the equation in logarithmic form: log base (7/8) y = x.
So, the logarithmic form of the given exponential function is log base (7/8) y = x.
To rewrite a logarithmic function as an exponential function, you need to use the following steps:
Step 1: Identify the base of the logarithmic function.
Step 2: Set the expression equal to y, as it represents the output (y-value) of the logarithmic function.
Step 3: Rewrite the equation in exponential form, using the base as the base of the exponent and the input (x-value) of the logarithmic function as the exponent.
Let's apply these steps to rewrite the logarithmic functions as exponential functions:
b) f(x) = log base 12 x
Step 1: The base of the logarithmic function is 12.
Step 2: Set the expression equal to y: y = log base 12 x.
Step 3: Rewrite the equation in exponential form: x = 12^y.
So, the exponential form of the given logarithmic function is x = 12^y.
c) f(x) = log base (5/9) x
Step 1: The base of the logarithmic function is 5/9.
Step 2: Set the expression equal to y: y = log base (5/9) x.
Step 3: Rewrite the equation in exponential form: x = (5/9)^y.
Therefore, the exponential form of the given logarithmic function is x = (5/9)^y.
memorize this pattern:
2^3 = 8 <-----> log2 8 = 3
once you know it, these questions become easy
e.g.
y = (7/8)^x <---> log(7/8) y = x
y = log 12x <---> 10^y = 12x
etc