If 0.3^x=ab, \log b=0.4, what is the value of x to the nearest tenth

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Answered question

2021-10-21

If
0.3x=ab,logb=0.4, what is the value of x to the nearest tenth

Answer & Explanation

FieniChoonin

FieniChoonin

Skilled2021-10-22Added 102 answers

Step 1
The logarithmic function is the inverse of the exponential function in a sense. This is because we have logex=x and elogx=x. So any exponential equation can be converted to an equivalent logarithmic equation and vice versa.
We will use the addition property of logarithms logab=loga+logb. We will use the exponent property of logarithms: logab=bloga. Convert the first equation to a logarithmic equation.
Step 2 We are given: 0.3x=ab,loga=0.3,logb=0.4. In the equation 0.3x=ab
Take log of both sides. Simplify and use the given data.
0.3x=ab
log0.3x=logab
xlog0.3=loga+logb
x=loga+logblog0.3
=0.3+0.4log0.3
=0.7log0.3
0.6
Hence, value of x is approximately -0.6.

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