Answer

Verified

341.1k+ views

**Hint:**Whenever the right and left side of the equation do not have the same base then in that case we should take “log” both the sides. The power rule is used to multiply the two logarithms and to combine the exponents. The exponential expression should be kept by itself on one side of the equation. The logarithms of both sides of the equation should be obtained and should be solved for variable.

**Complete step by step solution:**

A logarithm is an exponent that is written in a special way. A logarithm with base \[10\]is a common logarithm.

The product rule states that\[{\log _b}\left( {MN} \right) = {\log _b}\left( M \right) + {\log _b}\left( N\right)\].

This property denotes that logarithm of a product is the sum of the logs of its factors. The two numbers should be multiplied with the same base then the exponents must be added.

The quotient rule states that \[{\log _b}\left( {\frac{M}{N}} \right) = {\log _b}\left( M \right) + {\log_b}\left( N \right)\]

This property denotes that the log of a quotient is the difference of the log of the dividend and the divisor.

Since, the right and left side of the equation do not have the same base then in that case we should take “log” both the sides.

We have,

\[

{2^x} = 7 \\

\Rightarrow \log \left( {{2^x}} \right) = \log \left( 7 \right) \\

\]

Using the log property we have,

\[ \Rightarrow x\log \left( 2 \right) = \log \left( 7 \right)\]

Solving for “x” now we will have,

\[

\Rightarrow x = \dfrac{{\log \left( 7 \right)}}{{\log \left( 2 \right)}} \\

\Rightarrow x \approx 2.81 \\

\]

**Hence the solution of \[{2^x} = 7\] is\[ \approx 2.81\].**

**Note:**Start by the condensing the log expressions on the left into a single logarithm using the product rule. What we want is to have a single log expression on each side of the equation. Since we want to transform the left side into a single logarithmic equation, then we should use the product rule in reverse to condense it. Always check the solved values with the original logarithmic equations.

Recently Updated Pages

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

How do you arrange NH4 + BF3 H2O C2H2 in increasing class 11 chemistry CBSE

Is H mCT and q mCT the same thing If so which is more class 11 chemistry CBSE

What are the possible quantum number for the last outermost class 11 chemistry CBSE

Is C2 paramagnetic or diamagnetic class 11 chemistry CBSE

What happens when entropy reaches maximum class 11 chemistry JEE_Main

Trending doubts

How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Distinguish between the reserved forests and protected class 10 biology CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Give simple chemical tests to distinguish between the class 12 chemistry CBSE

Difference Between Plant Cell and Animal Cell

Which of the following books is not written by Harshavardhana class 6 social science CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

In which states of India are mango showers common What class 9 social science CBSE

What Made Mr Keesing Allow Anne to Talk in Class class 10 english CBSE