SOLUTION: 1.Can you write the logarithmic equation in exponential form? Log6 1/36 = -2 2.Can you write the exponential equation in logarithmic form? 64^1/2=8 3.Evaluate f(x)=logx a

Question 1072821: 1.Can you write the logarithmic equation in exponential form?
Log6 1/36 = -2
2.Can you write the exponential equation in logarithmic form?
64^1/2=8
3.Evaluate f(x)=logx at the indicated value of x. Round to three decimal places.
X=12.5
4.Evaluate the function at the indicated value of x=32.
F(x)log2x

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
1.Can you write the logarithmic equation in exponential form?

Log6 (1/36) = -2 = if and only if 6^(-2) = 1/36

6^(-2) is equivalent to 1/6^2

equation becomes:

1/6^2 = 1/36

simplify to get 1/36 = 1/36

2.Can you write the exponential equation in logarithmic form?

64^1/2=8 if and only if log64(8) = 1/2

log64(8) = log(8) / log(64) = .5 which is equal to 1/2

3.Evaluate f(x)=logx at the indicated value of x. Round to three decimal places.
X=12.5

log(12.5) = 1.096910013

log(12.5) = 1.096910013 if and only if 10^1.096910013 = 12.5

use your calculator to get 10^1.096910013 = 12.5, confirming the solution is correct.

4.Evaluate the function at the indicated value of x=32.
F(x) = log2x

y = log(2x) is equal to y = (2*32) when x = 32.

that becomes y = log(64) which makes y = 1.806179974

you could also solve as:

y = log(2x) is the same as y = log(2) + log(x) which is equal to y = log(2) + log(32) which is equal to y = .3010299957 + 1.505149978 which is finally equal to y = 1.806179974

some of the basic rules of logs and exponents are:

b^x = y if and only if logb(y) = x

the reverse is also true.

logb(y) = x if and only if b^x = y

someof the basic rules of logarithms are:

logb(x*y) = logb(x) + logb(y)

logb(x^y) = y * logb(x)

logb(x/y) = logb(x) - logb(y)

there are two log bases found in most scientific calculator.

they are log10(x) and loge(x)

log10(x) is normally shown as log(x).

the base of 10 is implied.

loge(x) is normally shown as ln(x).

the base called "e" is the scientific constant of 2.718281828.

here's a reference from wtamu college algebra.

http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/index.htm

tutorials 42 to 48 discuss exponential and logarithmic functions and the relationship between them.

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