Question

If log10 4 + log10 (4x + 1) = {log10 (x + 4)} + 1, then x is equal to

Answer 1

I think it will help you.....

Answer 2

Answer:

Value of x is 6

Step-by-step explanation:

The most practical method for expressing large numbers in mathematics is to use the logarithm. The power to which any number must be raised in order to reach certain values can be used as the definition of the logarithm. It's also said that logarithms are the opposite of exponentiation. In this article, we'll examine logarithmic functions, their characteristics, a log value table, and the log values from 1 to 10 for both log base 10 and log base e.

Product Rule:

In the product rule, two numbers will be multiplied with the same base and then the exponents will be added.

$logab=loga+logb$

Quotient Rule

In the quotient rule, two numbers will be divided with the same base and then the exponents will be subtracted.

$log\frac{a}{b} =loga-logb$

Power Rule

In the power rule, exponents' expressions are raised to power and then the exponents are multiplied.

$logA_{b} =blogA$

Given: $log_{10}4+log_{10}(4x+1)=log_{10}(x+4)+1$

Find: Value of x.

We know that $log_{10}10=1$

$log_{10}4+log_{10}(4x+1)=log_{10}(x+4)+1\\\Rightarrow log_{10} 4(4x+1)=log_{10} (x+4)10(\because logAB=logA+logB)\\\Rightarrow 16x+4=10x+40\\\Rightarrow 16x-10x=40-4\\\Rightarrow 6x=36\\\Rightarrow x=6$

Hence, value of x is 6.

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