Question

Wendell is looking over some data regarding the strength, measured in Pascals (Pa), of some building materials and how the strength relates to the length. The data are represented by the exponential function f(x) = 2x, where x is the length. Explain how he can convert this equation to a logarithmic function when strength is 8 Pascals

Answer 1

8 = 2^x
log 8 = log 2^x = xlog 2
log 2^3 = 3log 2 = xlog 2
x = 3

Answer 2

Can you explain please

Answer 3

ok

Answer 4

exponential equation:
nb=a

logarithmic equation: logna=b

Answer 5

@jonasjl

Answer 6

If you put in 8 for f(x) your exponential equation is
2x=8

Use the pattern above to change it to a log equation

Answer 7

@imqwerty

Answer 8

hey wait
is it \(f(x) = 2x\)
or is it this- \(f(x)=2^x\)

Answer 9

The second one

Answer 10

\(f(x)=2^x\)

^this is the given function and it is an exponential function
and here \(f(x)\) represents the strength

to make it a logarithmic function we just take "log" of both sides

so we have this-

\(log\left[f(x) \right] = log\left[2^x\right]\)

further we can write simplify it like this-

\(log\left[f(x) \right] = xlog\left[2\right]\)

\(\large \frac{log\left[f(x) \right]}{log\left[2\right]} = x\)

\(log_2\left[f(x) \right] = x\)

this function is now a logarithmic function

now its given that the strength \(\left[ f(x) \right]\) is 8
so
we can write this-

\(log_2(8)=x\)

you can simplify this to get x

Answer 11

x=3

Answer 12

yes correct :)

Answer 13

Thankkk youuu i have 4 other questions ill tag you

Answer 14

okay :)